ISL - Chapter 2 Labs

1 Chapter 2 Lab: Introduction to R

This one is indeed a soft intro!

No worry to make things wrong: TRY!

Got R?

• R can be downloaded from http://cran.r-project.org/

Start…

• an R script (tired!)
• an R Markdown document (wired!)

1.1 Basic commands

Functions are noted as funcname(input1, input2) - inputs are called arguments

Creating a vector by concatenating

c(1, 3, 2, 5)

## [1] 1 3 2 5

x <- c(1, 3, 2, 5) # use <- for assignment, leave = for parameter values
x

## [1] 1 3 2 5

x = c(1,6,2)
y = c(1,4,3)

Navigating history:

• up arrow
• ctrl + up (RStudio) while typing part of the command

Help:

• use ?
• help(funcname)

Length (of a vector)

length(x)

## [1] 3

length(y)

## [1] 3

Adding things together

1 + 4

## [1] 5

x + y # if same length

## [1]  2 10  5

x + 1

## [1] 2 7 3

x + c(1,2)

## Warning in x + c(1, 2): longer object length is not a multiple of shorter object
## length

## [1] 2 8 3

Listing objects, removing them

ls()

## [1] "x" "y"

rm(x, y)
ls()

## character(0)

Create a matrix of numbers

?matrix
x <- matrix(data=c(1,2,3,4), nrow=2, ncol=2)
x

##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4

x <- matrix(data=c(1,2,3,4), 2, 2)
x

##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4

# Recommended: specify arguments!
matrix(c(1,2,3,4),2,2,byrow=TRUE)

##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4

Squaring, squared root

x

##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4

sqrt(x)

##          [,1]     [,2]
## [1,] 1.000000 1.732051
## [2,] 1.414214 2.000000

sqrt(x)[,1]

## [1] 1.000000 1.414214

x^2

##      [,1] [,2]
## [1,]    1    9
## [2,]    4   16

Random normal variables, with rnorm

# bonus - when dealing with random quantities!
set.seed(42)

x <- rnorm(50)
# default: mean of 0 and standard deviation of 1
y <- x + rnorm(50,mean=50,sd=.1) 

Computing the correlation between two sets of numbers

cor(x,y)

## [1] 0.9968525

Mean & Standard deviation

mean(x)

## [1] -0.03567178

sd(x)

## [1] 1.151476

mean(y)

## [1] 49.9744

sd(y)

## [1] 1.132932

var(x)

## [1] 1.325898

var(y)

## [1] 1.283535

set.seed(3)
y <- rnorm(100)
mean(y)

## [1] 0.01103557

var(y)

## [1] 0.7328675

sqrt(var(y))

## [1] 0.8560768

sd(y)

## [1] 0.8560768

1.2 Graphics

Meet the plot() function!

plot(x,y)

?plot

The plot() function is the primary way to plot data in R. For instance, plot(x,y) produces a scatterplot of the numbers in x versus the numbers in y. There are many additional options that can be passed in to the plot() function. For example, passing in the argument xlab will result in a label on the x-axis. To find out more information about the plot() function, type ?plot.

set.seed(42)
x <- rnorm(100)
y <- rnorm(100)
plot(x,y)

plot(x,y,
     xlab="this is the x-axis",
     ylab="this is the y-axis",
     main="Plot of X vs Y")

# plot()

Saving the output:

open device
plot...
close device

pdf("Figure.pdf")
plot(x,y,col="green")
dev.off()

## quartz_off_screen 
##                 2

Devices: pdf(), jpeg(), …

Creating sequences of numbers

?seq
seq(0,1)

## [1] 0 1

seq(0,1,length=10)

##  [1] 0.0000000 0.1111111 0.2222222 0.3333333 0.4444444 0.5555556 0.6666667
##  [8] 0.7777778 0.8888889 1.0000000

pi

## [1] 3.141593

seq(-pi,pi,length=50)

##  [1] -3.14159265 -3.01336438 -2.88513611 -2.75690784 -2.62867957 -2.50045130
##  [7] -2.37222302 -2.24399475 -2.11576648 -1.98753821 -1.85930994 -1.73108167
## [13] -1.60285339 -1.47462512 -1.34639685 -1.21816858 -1.08994031 -0.96171204
## [19] -0.83348377 -0.70525549 -0.57702722 -0.44879895 -0.32057068 -0.19234241
## [25] -0.06411414  0.06411414  0.19234241  0.32057068  0.44879895  0.57702722
## [31]  0.70525549  0.83348377  0.96171204  1.08994031  1.21816858  1.34639685
## [37]  1.47462512  1.60285339  1.73108167  1.85930994  1.98753821  2.11576648
## [43]  2.24399475  2.37222302  2.50045130  2.62867957  2.75690784  2.88513611
## [49]  3.01336438  3.14159265

Some more complex plots:

• contour() to represent 3d data

?contour
?outer

# assignment and printing trick ;)
(x <- seq(-pi,pi,length=50))

##  [1] -3.14159265 -3.01336438 -2.88513611 -2.75690784 -2.62867957 -2.50045130
##  [7] -2.37222302 -2.24399475 -2.11576648 -1.98753821 -1.85930994 -1.73108167
## [13] -1.60285339 -1.47462512 -1.34639685 -1.21816858 -1.08994031 -0.96171204
## [19] -0.83348377 -0.70525549 -0.57702722 -0.44879895 -0.32057068 -0.19234241
## [25] -0.06411414  0.06411414  0.19234241  0.32057068  0.44879895  0.57702722
## [31]  0.70525549  0.83348377  0.96171204  1.08994031  1.21816858  1.34639685
## [37]  1.47462512  1.60285339  1.73108167  1.85930994  1.98753821  2.11576648
## [43]  2.24399475  2.37222302  2.50045130  2.62867957  2.75690784  2.88513611
## [49]  3.01336438  3.14159265

y <- x
f <- outer(x,y,function (x,y)cos(y)/(1+x^2))
f

##              [,1]        [,2]        [,3]        [,4]        [,5]        [,6]
##  [1,] -0.09199967 -0.09124435 -0.08899081 -0.08527603 -0.08016103 -0.07372979
##  [2,] -0.09920276 -0.09838830 -0.09595832 -0.09195270 -0.08643722 -0.07950244
##  [3,] -0.10724999 -0.10636947 -0.10374236 -0.09941181 -0.09344892 -0.08595160
##  [4,] -0.11627176 -0.11531717 -0.11246907 -0.10777424 -0.10130976 -0.09318177
##  [5,] -0.12642295 -0.12538502 -0.12228827 -0.11718355 -0.11015468 -0.10131707
##  [6,] -0.13788811 -0.13675606 -0.13337846 -0.12781080 -0.12014449 -0.11050541
##  [7,] -0.15088778 -0.14964899 -0.14595297 -0.13986041 -0.13147134 -0.12092352
##  [8,] -0.16568601 -0.16432573 -0.16026723 -0.15357714 -0.14436532 -0.13278303
##  [9,] -0.18259945 -0.18110031 -0.17662751 -0.16925449 -0.15910231 -0.14633769
## [10,] -0.20200763 -0.20034915 -0.19540094 -0.18724425 -0.17601302 -0.16189166
## [11,] -0.22436448 -0.22252245 -0.21702661 -0.20796720 -0.19549297 -0.17980875
## [12,] -0.25020994 -0.24815572 -0.24202679 -0.23192379 -0.21801260 -0.20052166
## [13,] -0.28017962 -0.27787935 -0.27101630 -0.25970318 -0.24412574 -0.22453976
## [14,] -0.31500833 -0.31242211 -0.30470594 -0.29198650 -0.27447265 -0.25245196
## [15,] -0.35551960 -0.35260078 -0.34389228 -0.32953707 -0.30977087 -0.28491825
## [16,] -0.40258707 -0.39928184 -0.38942041 -0.37316471 -0.35078165 -0.32263877
## [17,] -0.45704468 -0.45329235 -0.44209697 -0.42364238 -0.39823158 -0.36628184
## [18,] -0.51951019 -0.51524502 -0.50251954 -0.48154270 -0.45265895 -0.41634255
## [19,] -0.59007662 -0.58523209 -0.57077808 -0.54695190 -0.51414479 -0.47289544
## [20,] -0.66783078 -0.66234790 -0.64598928 -0.61902354 -0.58189345 -0.53520868
## [21,] -0.75020983 -0.74405061 -0.72567411 -0.69538206 -0.65367185 -0.60122837
## [22,] -0.83234804 -0.82551448 -0.80512599 -0.77151735 -0.72524042 -0.66705506
## [23,] -0.90681105 -0.89936615 -0.87715367 -0.84053836 -0.79012143 -0.72673073
## [24,] -0.96432424 -0.95640716 -0.93278589 -0.89384830 -0.84023375 -0.77282259
## [25,] -0.99590621 -0.98772983 -0.96333496 -0.92312215 -0.86775170 -0.79813280
## [26,] -0.99590621 -0.98772983 -0.96333496 -0.92312215 -0.86775170 -0.79813280
## [27,] -0.96432424 -0.95640716 -0.93278589 -0.89384830 -0.84023375 -0.77282259
## [28,] -0.90681105 -0.89936615 -0.87715367 -0.84053836 -0.79012143 -0.72673073
## [29,] -0.83234804 -0.82551448 -0.80512599 -0.77151735 -0.72524042 -0.66705506
## [30,] -0.75020983 -0.74405061 -0.72567411 -0.69538206 -0.65367185 -0.60122837
## [31,] -0.66783078 -0.66234790 -0.64598928 -0.61902354 -0.58189345 -0.53520868
## [32,] -0.59007662 -0.58523209 -0.57077808 -0.54695190 -0.51414479 -0.47289544
## [33,] -0.51951019 -0.51524502 -0.50251954 -0.48154270 -0.45265895 -0.41634255
## [34,] -0.45704468 -0.45329235 -0.44209697 -0.42364238 -0.39823158 -0.36628184
## [35,] -0.40258707 -0.39928184 -0.38942041 -0.37316471 -0.35078165 -0.32263877
## [36,] -0.35551960 -0.35260078 -0.34389228 -0.32953707 -0.30977087 -0.28491825
## [37,] -0.31500833 -0.31242211 -0.30470594 -0.29198650 -0.27447265 -0.25245196
## [38,] -0.28017962 -0.27787935 -0.27101630 -0.25970318 -0.24412574 -0.22453976
## [39,] -0.25020994 -0.24815572 -0.24202679 -0.23192379 -0.21801260 -0.20052166
## [40,] -0.22436448 -0.22252245 -0.21702661 -0.20796720 -0.19549297 -0.17980875
## [41,] -0.20200763 -0.20034915 -0.19540094 -0.18724425 -0.17601302 -0.16189166
## [42,] -0.18259945 -0.18110031 -0.17662751 -0.16925449 -0.15910231 -0.14633769
## [43,] -0.16568601 -0.16432573 -0.16026723 -0.15357714 -0.14436532 -0.13278303
## [44,] -0.15088778 -0.14964899 -0.14595297 -0.13986041 -0.13147134 -0.12092352
## [45,] -0.13788811 -0.13675606 -0.13337846 -0.12781080 -0.12014449 -0.11050541
## [46,] -0.12642295 -0.12538502 -0.12228827 -0.11718355 -0.11015468 -0.10131707
## [47,] -0.11627176 -0.11531717 -0.11246907 -0.10777424 -0.10130976 -0.09318177
## [48,] -0.10724999 -0.10636947 -0.10374236 -0.09941181 -0.09344892 -0.08595160
## [49,] -0.09920276 -0.09838830 -0.09595832 -0.09195270 -0.08643722 -0.07950244
## [50,] -0.09199967 -0.09124435 -0.08899081 -0.08527603 -0.08016103 -0.07372979
##              [,7]        [,8]        [,9]       [,10]       [,11]       [,12]
##  [1,] -0.06608790 -0.05736085 -0.04769194 -0.03723993 -0.02617644 -0.01468314
##  [2,] -0.07126224 -0.06185191 -0.05142597 -0.04015562 -0.02822592 -0.01583275
##  [3,] -0.07704296 -0.06686927 -0.05559760 -0.04341301 -0.03051558 -0.01711709
##  [4,] -0.08352374 -0.07249426 -0.06027442 -0.04706487 -0.03308252 -0.01855696
##  [5,] -0.09081584 -0.07882342 -0.06553672 -0.05117390 -0.03597082 -0.02017709
##  [6,] -0.09905184 -0.08597183 -0.07148017 -0.05581481 -0.03923297 -0.02200693
##  [7,] -0.10839014 -0.09407699 -0.07821910 -0.06107686 -0.04293173 -0.02408167
##  [8,] -0.11902044 -0.10330354 -0.08589040 -0.06706694 -0.04714224 -0.02644347
##  [9,] -0.13117020 -0.11384889 -0.09465820 -0.07391322 -0.05195458 -0.02914285
## [10,] -0.14511205 -0.12594970 -0.10471925 -0.08176932 -0.05747674 -0.03224040
## [11,] -0.16117208 -0.13988897 -0.11630888 -0.09081901 -0.06383788 -0.03580855
## [12,] -0.17973815 -0.15600335 -0.12970697 -0.10128082 -0.07119163 -0.03993348
## [13,] -0.20126685 -0.17468913 -0.14524303 -0.11341204 -0.07971883 -0.04471664
## [14,] -0.22628603 -0.19640448 -0.16329798 -0.12751012 -0.08962856 -0.05027530
## [15,] -0.25538727 -0.22166284 -0.18429872 -0.14390841 -0.10115513 -0.05674089
## [16,] -0.28919816 -0.25100894 -0.20869815 -0.16296054 -0.11454713 -0.06425285
## [17,] -0.32831775 -0.28496270 -0.23692857 -0.18500408 -0.13004182 -0.07294428
## [18,] -0.37318981 -0.32390931 -0.26931022 -0.21028907 -0.14781498 -0.08291377
## [19,] -0.42388115 -0.36790675 -0.30589133 -0.23885319 -0.16789308 -0.09417617
## [20,] -0.47973581 -0.41638568 -0.34619851 -0.27032678 -0.19001628 -0.10658572
## [21,] -0.53891274 -0.46774818 -0.38890320 -0.30367244 -0.21345539 -0.11973341
## [22,] -0.59791668 -0.51896052 -0.43148304 -0.33692062 -0.23682598 -0.13284266
## [23,] -0.65140713 -0.56538744 -0.47008411 -0.36706201 -0.25801276 -0.14472695
## [24,] -0.69272169 -0.60124633 -0.49989852 -0.39034239 -0.27437685 -0.15390605
## [25,] -0.71540858 -0.62093736 -0.51627038 -0.40312624 -0.28336279 -0.15894653
## [26,] -0.71540858 -0.62093736 -0.51627038 -0.40312624 -0.28336279 -0.15894653
## [27,] -0.69272169 -0.60124633 -0.49989852 -0.39034239 -0.27437685 -0.15390605
## [28,] -0.65140713 -0.56538744 -0.47008411 -0.36706201 -0.25801276 -0.14472695
## [29,] -0.59791668 -0.51896052 -0.43148304 -0.33692062 -0.23682598 -0.13284266
## [30,] -0.53891274 -0.46774818 -0.38890320 -0.30367244 -0.21345539 -0.11973341
## [31,] -0.47973581 -0.41638568 -0.34619851 -0.27032678 -0.19001628 -0.10658572
## [32,] -0.42388115 -0.36790675 -0.30589133 -0.23885319 -0.16789308 -0.09417617
## [33,] -0.37318981 -0.32390931 -0.26931022 -0.21028907 -0.14781498 -0.08291377
## [34,] -0.32831775 -0.28496270 -0.23692857 -0.18500408 -0.13004182 -0.07294428
## [35,] -0.28919816 -0.25100894 -0.20869815 -0.16296054 -0.11454713 -0.06425285
## [36,] -0.25538727 -0.22166284 -0.18429872 -0.14390841 -0.10115513 -0.05674089
## [37,] -0.22628603 -0.19640448 -0.16329798 -0.12751012 -0.08962856 -0.05027530
## [38,] -0.20126685 -0.17468913 -0.14524303 -0.11341204 -0.07971883 -0.04471664
## [39,] -0.17973815 -0.15600335 -0.12970697 -0.10128082 -0.07119163 -0.03993348
## [40,] -0.16117208 -0.13988897 -0.11630888 -0.09081901 -0.06383788 -0.03580855
## [41,] -0.14511205 -0.12594970 -0.10471925 -0.08176932 -0.05747674 -0.03224040
## [42,] -0.13117020 -0.11384889 -0.09465820 -0.07391322 -0.05195458 -0.02914285
## [43,] -0.11902044 -0.10330354 -0.08589040 -0.06706694 -0.04714224 -0.02644347
## [44,] -0.10839014 -0.09407699 -0.07821910 -0.06107686 -0.04293173 -0.02408167
## [45,] -0.09905184 -0.08597183 -0.07148017 -0.05581481 -0.03923297 -0.02200693
## [46,] -0.09081584 -0.07882342 -0.06553672 -0.05117390 -0.03597082 -0.02017709
## [47,] -0.08352374 -0.07249426 -0.06027442 -0.04706487 -0.03308252 -0.01855696
## [48,] -0.07704296 -0.06686927 -0.05559760 -0.04341301 -0.03051558 -0.01711709
## [49,] -0.07126224 -0.06185191 -0.05142597 -0.04015562 -0.02822592 -0.01583275
## [50,] -0.06608790 -0.05736085 -0.04769194 -0.03723993 -0.02617644 -0.01468314
##              [,13]       [,14]      [,15]      [,16]      [,17]      [,18]
##  [1,] -0.002948735 0.008834087 0.02047185 0.03177347 0.04255337 0.05263454
##  [2,] -0.003179605 0.009525749 0.02207469 0.03426117 0.04588507 0.05675555
##  [3,] -0.003437531 0.010298468 0.02386537 0.03704040 0.04960723 0.06135950
##  [4,] -0.003726693 0.011164766 0.02587290 0.04015620 0.05378014 0.06652101
##  [5,] -0.004052055 0.012139514 0.02813175 0.04366207 0.05847545 0.07232868
##  [6,] -0.004419532 0.013240434 0.03068299 0.04762174 0.06377853 0.07888809
##  [7,] -0.004836191 0.014488701 0.03357569 0.05211137 0.06979137 0.08632541
##  [8,] -0.005310498 0.015909672 0.03686861 0.05722216 0.07663613 0.09479173
##  [9,] -0.005852600 0.017533752 0.04063220 0.06306347 0.08445924 0.10446819
## [10,] -0.006474663 0.019397384 0.04495093 0.06976638 0.09343626 0.11557193
## [11,] -0.007191236 0.021544156 0.04992579 0.07748765 0.10377716 0.12836266
## [12,] -0.008019623 0.024025916 0.05567695 0.08641377 0.11573168 0.14314928
## [13,] -0.008980199 0.026903695 0.06234583 0.09676425 0.12959380 0.16029543
## [14,] -0.010096514 0.030248053 0.07009595 0.10879287 0.14570341 0.18022151
## [15,] -0.011394964 0.034138067 0.07911055 0.12278404 0.16444143 0.20339868
## [16,] -0.012903551 0.038657629 0.08958405 0.13903951 0.18621194 0.23032677
## [17,] -0.014649003 0.043886814 0.10170201 0.15784726 0.21140067 0.26148288
## [18,] -0.016651121 0.049884941 0.11560189 0.17942067 0.24029336 0.29722044
## [19,] -0.018912886 0.056660942 0.13130440 0.20379184 0.27293303 0.33759266
## [20,] -0.021405030 0.064127132 0.14860633 0.23064541 0.30889731 0.38207712
## [21,] -0.024045408 0.072037417 0.16693739 0.25909626 0.34700077 0.42920754
## [22,] -0.026678068 0.079924578 0.18521486 0.28746393 0.38499284 0.47620018
## [23,] -0.029064725 0.087074741 0.20178444 0.31318085 0.41943483 0.51880171
## [24,] -0.030908113 0.092597332 0.21458233 0.33304390 0.44603689 0.55170597
## [25,] -0.031920365 0.095629927 0.22160998 0.34395120 0.46064475 0.56977453
## [26,] -0.031920365 0.095629927 0.22160998 0.34395120 0.46064475 0.56977453
## [27,] -0.030908113 0.092597332 0.21458233 0.33304390 0.44603689 0.55170597
## [28,] -0.029064725 0.087074741 0.20178444 0.31318085 0.41943483 0.51880171
## [29,] -0.026678068 0.079924578 0.18521486 0.28746393 0.38499284 0.47620018
## [30,] -0.024045408 0.072037417 0.16693739 0.25909626 0.34700077 0.42920754
## [31,] -0.021405030 0.064127132 0.14860633 0.23064541 0.30889731 0.38207712
## [32,] -0.018912886 0.056660942 0.13130440 0.20379184 0.27293303 0.33759266
## [33,] -0.016651121 0.049884941 0.11560189 0.17942067 0.24029336 0.29722044
## [34,] -0.014649003 0.043886814 0.10170201 0.15784726 0.21140067 0.26148288
## [35,] -0.012903551 0.038657629 0.08958405 0.13903951 0.18621194 0.23032677
## [36,] -0.011394964 0.034138067 0.07911055 0.12278404 0.16444143 0.20339868
## [37,] -0.010096514 0.030248053 0.07009595 0.10879287 0.14570341 0.18022151
## [38,] -0.008980199 0.026903695 0.06234583 0.09676425 0.12959380 0.16029543
## [39,] -0.008019623 0.024025916 0.05567695 0.08641377 0.11573168 0.14314928
## [40,] -0.007191236 0.021544156 0.04992579 0.07748765 0.10377716 0.12836266
## [41,] -0.006474663 0.019397384 0.04495093 0.06976638 0.09343626 0.11557193
## [42,] -0.005852600 0.017533752 0.04063220 0.06306347 0.08445924 0.10446819
## [43,] -0.005310498 0.015909672 0.03686861 0.05722216 0.07663613 0.09479173
## [44,] -0.004836191 0.014488701 0.03357569 0.05211137 0.06979137 0.08632541
## [45,] -0.004419532 0.013240434 0.03068299 0.04762174 0.06377853 0.07888809
## [46,] -0.004052055 0.012139514 0.02813175 0.04366207 0.05847545 0.07232868
## [47,] -0.003726693 0.011164766 0.02587290 0.04015620 0.05378014 0.06652101
## [48,] -0.003437531 0.010298468 0.02386537 0.03704040 0.04960723 0.06135950
## [49,] -0.003179605 0.009525749 0.02207469 0.03426117 0.04588507 0.05675555
## [50,] -0.002948735 0.008834087 0.02047185 0.03177347 0.04255337 0.05263454
##            [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
##  [1,] 0.06185146 0.07005278 0.07710383 0.08288884 0.08731281 0.09030312
##  [2,] 0.06669410 0.07553754 0.08314065 0.08937860 0.09414895 0.09737338
##  [3,] 0.07210426 0.08166507 0.08988494 0.09662890 0.10178622 0.10527221
##  [4,] 0.07816961 0.08853466 0.09744598 0.10475723 0.11034838 0.11412761
##  [5,] 0.08499426 0.09626424 0.10595357 0.11390314 0.11998243 0.12409160
##  [6,] 0.09270230 0.10499435 0.11556239 0.12423290 0.13086351 0.13534534
##  [7,] 0.10144199 0.11489289 0.12645725 0.13594519 0.14320091 0.14810528
##  [8,] 0.11139085 0.12616095 0.13885948 0.14927794 0.15724526 0.16263062
##  [9,] 0.12276177 0.13903961 0.15303443 0.16451642 0.17329706 0.17923216
## [10,] 0.13580991 0.15381789 0.16930019 0.18200258 0.19171650 0.19828244
## [11,] 0.15084044 0.17084143 0.18803720 0.20214541 0.21293440 0.22022701
## [12,] 0.16821637 0.19052135 0.20969798 0.22543137 0.23746318 0.24559586
## [13,] 0.18836501 0.21334164 0.23481520 0.25243311 0.26590608 0.27501287
## [14,] 0.21178038 0.23986182 0.26400473 0.28381270 0.29896046 0.30919931
## [15,] 0.23901614 0.27070896 0.29795674 0.32031209 0.33740791 0.34896351
## [16,] 0.27065965 0.30654830 0.33740344 0.36271842 0.38207758 0.39516303
## [17,] 0.30727155 0.34801483 0.38304371 0.41178303 0.43376088 0.44861639
## [18,] 0.34926717 0.39557894 0.43539531 0.46806251 0.49304414 0.50992999
## [19,] 0.39670903 0.44931145 0.49453619 0.53164066 0.56001560 0.57919511
## [20,] 0.44898323 0.50851705 0.55970103 0.60169474 0.63380864 0.65551542
## [21,] 0.50436673 0.57124424 0.62874193 0.67591570 0.71199095 0.73637532
## [22,] 0.55958833 0.63378805 0.69758099 0.74991967 0.78994469 0.81699884
## [23,] 0.60964988 0.69048761 0.75998756 0.81700853 0.86061424 0.89008869
## [24,] 0.64831605 0.73428080 0.80818868 0.86882612 0.91519747 0.94654129
## [25,] 0.66954863 0.75832876 0.83465714 0.89728049 0.94517051 0.97754086
## [26,] 0.66954863 0.75832876 0.83465714 0.89728049 0.94517051 0.97754086
## [27,] 0.64831605 0.73428080 0.80818868 0.86882612 0.91519747 0.94654129
## [28,] 0.60964988 0.69048761 0.75998756 0.81700853 0.86061424 0.89008869
## [29,] 0.55958833 0.63378805 0.69758099 0.74991967 0.78994469 0.81699884
## [30,] 0.50436673 0.57124424 0.62874193 0.67591570 0.71199095 0.73637532
## [31,] 0.44898323 0.50851705 0.55970103 0.60169474 0.63380864 0.65551542
## [32,] 0.39670903 0.44931145 0.49453619 0.53164066 0.56001560 0.57919511
## [33,] 0.34926717 0.39557894 0.43539531 0.46806251 0.49304414 0.50992999
## [34,] 0.30727155 0.34801483 0.38304371 0.41178303 0.43376088 0.44861639
## [35,] 0.27065965 0.30654830 0.33740344 0.36271842 0.38207758 0.39516303
## [36,] 0.23901614 0.27070896 0.29795674 0.32031209 0.33740791 0.34896351
## [37,] 0.21178038 0.23986182 0.26400473 0.28381270 0.29896046 0.30919931
## [38,] 0.18836501 0.21334164 0.23481520 0.25243311 0.26590608 0.27501287
## [39,] 0.16821637 0.19052135 0.20969798 0.22543137 0.23746318 0.24559586
## [40,] 0.15084044 0.17084143 0.18803720 0.20214541 0.21293440 0.22022701
## [41,] 0.13580991 0.15381789 0.16930019 0.18200258 0.19171650 0.19828244
## [42,] 0.12276177 0.13903961 0.15303443 0.16451642 0.17329706 0.17923216
## [43,] 0.11139085 0.12616095 0.13885948 0.14927794 0.15724526 0.16263062
## [44,] 0.10144199 0.11489289 0.12645725 0.13594519 0.14320091 0.14810528
## [45,] 0.09270230 0.10499435 0.11556239 0.12423290 0.13086351 0.13534534
## [46,] 0.08499426 0.09626424 0.10595357 0.11390314 0.11998243 0.12409160
## [47,] 0.07816961 0.08853466 0.09744598 0.10475723 0.11034838 0.11412761
## [48,] 0.07210426 0.08166507 0.08988494 0.09662890 0.10178622 0.10527221
## [49,] 0.06669410 0.07553754 0.08314065 0.08937860 0.09414895 0.09737338
## [50,] 0.06185146 0.07005278 0.07710383 0.08288884 0.08731281 0.09030312
##            [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
##  [1,] 0.09181065 0.09181065 0.09030312 0.08731281 0.08288884 0.07710383
##  [2,] 0.09899894 0.09899894 0.09737338 0.09414895 0.08937860 0.08314065
##  [3,] 0.10702963 0.10702963 0.10527221 0.10178622 0.09662890 0.08988494
##  [4,] 0.11603286 0.11603286 0.11412761 0.11034838 0.10475723 0.09744598
##  [5,] 0.12616320 0.12616320 0.12409160 0.11998243 0.11390314 0.10595357
##  [6,] 0.13760481 0.13760481 0.13534534 0.13086351 0.12423290 0.11556239
##  [7,] 0.15057776 0.15057776 0.14810528 0.14320091 0.13594519 0.12645725
##  [8,] 0.16534559 0.16534559 0.16263062 0.15724526 0.14927794 0.13885948
##  [9,] 0.18222428 0.18222428 0.17923216 0.17329706 0.16451642 0.15303443
## [10,] 0.20159258 0.20159258 0.19828244 0.19171650 0.18200258 0.16930019
## [11,] 0.22390350 0.22390350 0.22022701 0.21293440 0.20214541 0.18803720
## [12,] 0.24969586 0.24969586 0.24559586 0.23746318 0.22543137 0.20969798
## [13,] 0.27960396 0.27960396 0.27501287 0.26590608 0.25243311 0.23481520
## [14,] 0.31436111 0.31436111 0.30919931 0.29896046 0.28381270 0.26400473
## [15,] 0.35478914 0.35478914 0.34896351 0.33740791 0.32031209 0.29795674
## [16,] 0.40175992 0.40175992 0.39516303 0.38207758 0.36271842 0.33740344
## [17,] 0.45610564 0.45610564 0.44861639 0.43376088 0.41178303 0.38304371
## [18,] 0.51844281 0.51844281 0.50992999 0.49304414 0.46806251 0.43539531
## [19,] 0.58886424 0.58886424 0.57919511 0.56001560 0.53164066 0.49453619
## [20,] 0.66645865 0.66645865 0.65551542 0.63380864 0.60169474 0.55970103
## [21,] 0.74866844 0.74866844 0.73637532 0.71199095 0.67591570 0.62874193
## [22,] 0.83063789 0.83063789 0.81699884 0.78994469 0.74991967 0.69758099
## [23,] 0.90494791 0.90494791 0.89008869 0.86061424 0.81700853 0.75998756
## [24,] 0.96234294 0.96234294 0.94654129 0.91519747 0.86882612 0.80818868
## [25,] 0.99386001 0.99386001 0.97754086 0.94517051 0.89728049 0.83465714
## [26,] 0.99386001 0.99386001 0.97754086 0.94517051 0.89728049 0.83465714
## [27,] 0.96234294 0.96234294 0.94654129 0.91519747 0.86882612 0.80818868
## [28,] 0.90494791 0.90494791 0.89008869 0.86061424 0.81700853 0.75998756
## [29,] 0.83063789 0.83063789 0.81699884 0.78994469 0.74991967 0.69758099
## [30,] 0.74866844 0.74866844 0.73637532 0.71199095 0.67591570 0.62874193
## [31,] 0.66645865 0.66645865 0.65551542 0.63380864 0.60169474 0.55970103
## [32,] 0.58886424 0.58886424 0.57919511 0.56001560 0.53164066 0.49453619
## [33,] 0.51844281 0.51844281 0.50992999 0.49304414 0.46806251 0.43539531
## [34,] 0.45610564 0.45610564 0.44861639 0.43376088 0.41178303 0.38304371
## [35,] 0.40175992 0.40175992 0.39516303 0.38207758 0.36271842 0.33740344
## [36,] 0.35478914 0.35478914 0.34896351 0.33740791 0.32031209 0.29795674
## [37,] 0.31436111 0.31436111 0.30919931 0.29896046 0.28381270 0.26400473
## [38,] 0.27960396 0.27960396 0.27501287 0.26590608 0.25243311 0.23481520
## [39,] 0.24969586 0.24969586 0.24559586 0.23746318 0.22543137 0.20969798
## [40,] 0.22390350 0.22390350 0.22022701 0.21293440 0.20214541 0.18803720
## [41,] 0.20159258 0.20159258 0.19828244 0.19171650 0.18200258 0.16930019
## [42,] 0.18222428 0.18222428 0.17923216 0.17329706 0.16451642 0.15303443
## [43,] 0.16534559 0.16534559 0.16263062 0.15724526 0.14927794 0.13885948
## [44,] 0.15057776 0.15057776 0.14810528 0.14320091 0.13594519 0.12645725
## [45,] 0.13760481 0.13760481 0.13534534 0.13086351 0.12423290 0.11556239
## [46,] 0.12616320 0.12616320 0.12409160 0.11998243 0.11390314 0.10595357
## [47,] 0.11603286 0.11603286 0.11412761 0.11034838 0.10475723 0.09744598
## [48,] 0.10702963 0.10702963 0.10527221 0.10178622 0.09662890 0.08988494
## [49,] 0.09899894 0.09899894 0.09737338 0.09414895 0.08937860 0.08314065
## [50,] 0.09181065 0.09181065 0.09030312 0.08731281 0.08288884 0.07710383
##            [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
##  [1,] 0.07005278 0.06185146 0.05263454 0.04255337 0.03177347 0.02047185
##  [2,] 0.07553754 0.06669410 0.05675555 0.04588507 0.03426117 0.02207469
##  [3,] 0.08166507 0.07210426 0.06135950 0.04960723 0.03704040 0.02386537
##  [4,] 0.08853466 0.07816961 0.06652101 0.05378014 0.04015620 0.02587290
##  [5,] 0.09626424 0.08499426 0.07232868 0.05847545 0.04366207 0.02813175
##  [6,] 0.10499435 0.09270230 0.07888809 0.06377853 0.04762174 0.03068299
##  [7,] 0.11489289 0.10144199 0.08632541 0.06979137 0.05211137 0.03357569
##  [8,] 0.12616095 0.11139085 0.09479173 0.07663613 0.05722216 0.03686861
##  [9,] 0.13903961 0.12276177 0.10446819 0.08445924 0.06306347 0.04063220
## [10,] 0.15381789 0.13580991 0.11557193 0.09343626 0.06976638 0.04495093
## [11,] 0.17084143 0.15084044 0.12836266 0.10377716 0.07748765 0.04992579
## [12,] 0.19052135 0.16821637 0.14314928 0.11573168 0.08641377 0.05567695
## [13,] 0.21334164 0.18836501 0.16029543 0.12959380 0.09676425 0.06234583
## [14,] 0.23986182 0.21178038 0.18022151 0.14570341 0.10879287 0.07009595
## [15,] 0.27070896 0.23901614 0.20339868 0.16444143 0.12278404 0.07911055
## [16,] 0.30654830 0.27065965 0.23032677 0.18621194 0.13903951 0.08958405
## [17,] 0.34801483 0.30727155 0.26148288 0.21140067 0.15784726 0.10170201
## [18,] 0.39557894 0.34926717 0.29722044 0.24029336 0.17942067 0.11560189
## [19,] 0.44931145 0.39670903 0.33759266 0.27293303 0.20379184 0.13130440
## [20,] 0.50851705 0.44898323 0.38207712 0.30889731 0.23064541 0.14860633
## [21,] 0.57124424 0.50436673 0.42920754 0.34700077 0.25909626 0.16693739
## [22,] 0.63378805 0.55958833 0.47620018 0.38499284 0.28746393 0.18521486
## [23,] 0.69048761 0.60964988 0.51880171 0.41943483 0.31318085 0.20178444
## [24,] 0.73428080 0.64831605 0.55170597 0.44603689 0.33304390 0.21458233
## [25,] 0.75832876 0.66954863 0.56977453 0.46064475 0.34395120 0.22160998
## [26,] 0.75832876 0.66954863 0.56977453 0.46064475 0.34395120 0.22160998
## [27,] 0.73428080 0.64831605 0.55170597 0.44603689 0.33304390 0.21458233
## [28,] 0.69048761 0.60964988 0.51880171 0.41943483 0.31318085 0.20178444
## [29,] 0.63378805 0.55958833 0.47620018 0.38499284 0.28746393 0.18521486
## [30,] 0.57124424 0.50436673 0.42920754 0.34700077 0.25909626 0.16693739
## [31,] 0.50851705 0.44898323 0.38207712 0.30889731 0.23064541 0.14860633
## [32,] 0.44931145 0.39670903 0.33759266 0.27293303 0.20379184 0.13130440
## [33,] 0.39557894 0.34926717 0.29722044 0.24029336 0.17942067 0.11560189
## [34,] 0.34801483 0.30727155 0.26148288 0.21140067 0.15784726 0.10170201
## [35,] 0.30654830 0.27065965 0.23032677 0.18621194 0.13903951 0.08958405
## [36,] 0.27070896 0.23901614 0.20339868 0.16444143 0.12278404 0.07911055
## [37,] 0.23986182 0.21178038 0.18022151 0.14570341 0.10879287 0.07009595
## [38,] 0.21334164 0.18836501 0.16029543 0.12959380 0.09676425 0.06234583
## [39,] 0.19052135 0.16821637 0.14314928 0.11573168 0.08641377 0.05567695
## [40,] 0.17084143 0.15084044 0.12836266 0.10377716 0.07748765 0.04992579
## [41,] 0.15381789 0.13580991 0.11557193 0.09343626 0.06976638 0.04495093
## [42,] 0.13903961 0.12276177 0.10446819 0.08445924 0.06306347 0.04063220
## [43,] 0.12616095 0.11139085 0.09479173 0.07663613 0.05722216 0.03686861
## [44,] 0.11489289 0.10144199 0.08632541 0.06979137 0.05211137 0.03357569
## [45,] 0.10499435 0.09270230 0.07888809 0.06377853 0.04762174 0.03068299
## [46,] 0.09626424 0.08499426 0.07232868 0.05847545 0.04366207 0.02813175
## [47,] 0.08853466 0.07816961 0.06652101 0.05378014 0.04015620 0.02587290
## [48,] 0.08166507 0.07210426 0.06135950 0.04960723 0.03704040 0.02386537
## [49,] 0.07553754 0.06669410 0.05675555 0.04588507 0.03426117 0.02207469
## [50,] 0.07005278 0.06185146 0.05263454 0.04255337 0.03177347 0.02047185
##             [,37]        [,38]       [,39]       [,40]       [,41]       [,42]
##  [1,] 0.008834087 -0.002948735 -0.01468314 -0.02617644 -0.03723993 -0.04769194
##  [2,] 0.009525749 -0.003179605 -0.01583275 -0.02822592 -0.04015562 -0.05142597
##  [3,] 0.010298468 -0.003437531 -0.01711709 -0.03051558 -0.04341301 -0.05559760
##  [4,] 0.011164766 -0.003726693 -0.01855696 -0.03308252 -0.04706487 -0.06027442
##  [5,] 0.012139514 -0.004052055 -0.02017709 -0.03597082 -0.05117390 -0.06553672
##  [6,] 0.013240434 -0.004419532 -0.02200693 -0.03923297 -0.05581481 -0.07148017
##  [7,] 0.014488701 -0.004836191 -0.02408167 -0.04293173 -0.06107686 -0.07821910
##  [8,] 0.015909672 -0.005310498 -0.02644347 -0.04714224 -0.06706694 -0.08589040
##  [9,] 0.017533752 -0.005852600 -0.02914285 -0.05195458 -0.07391322 -0.09465820
## [10,] 0.019397384 -0.006474663 -0.03224040 -0.05747674 -0.08176932 -0.10471925
## [11,] 0.021544156 -0.007191236 -0.03580855 -0.06383788 -0.09081901 -0.11630888
## [12,] 0.024025916 -0.008019623 -0.03993348 -0.07119163 -0.10128082 -0.12970697
## [13,] 0.026903695 -0.008980199 -0.04471664 -0.07971883 -0.11341204 -0.14524303
## [14,] 0.030248053 -0.010096514 -0.05027530 -0.08962856 -0.12751012 -0.16329798
## [15,] 0.034138067 -0.011394964 -0.05674089 -0.10115513 -0.14390841 -0.18429872
## [16,] 0.038657629 -0.012903551 -0.06425285 -0.11454713 -0.16296054 -0.20869815
## [17,] 0.043886814 -0.014649003 -0.07294428 -0.13004182 -0.18500408 -0.23692857
## [18,] 0.049884941 -0.016651121 -0.08291377 -0.14781498 -0.21028907 -0.26931022
## [19,] 0.056660942 -0.018912886 -0.09417617 -0.16789308 -0.23885319 -0.30589133
## [20,] 0.064127132 -0.021405030 -0.10658572 -0.19001628 -0.27032678 -0.34619851
## [21,] 0.072037417 -0.024045408 -0.11973341 -0.21345539 -0.30367244 -0.38890320
## [22,] 0.079924578 -0.026678068 -0.13284266 -0.23682598 -0.33692062 -0.43148304
## [23,] 0.087074741 -0.029064725 -0.14472695 -0.25801276 -0.36706201 -0.47008411
## [24,] 0.092597332 -0.030908113 -0.15390605 -0.27437685 -0.39034239 -0.49989852
## [25,] 0.095629927 -0.031920365 -0.15894653 -0.28336279 -0.40312624 -0.51627038
## [26,] 0.095629927 -0.031920365 -0.15894653 -0.28336279 -0.40312624 -0.51627038
## [27,] 0.092597332 -0.030908113 -0.15390605 -0.27437685 -0.39034239 -0.49989852
## [28,] 0.087074741 -0.029064725 -0.14472695 -0.25801276 -0.36706201 -0.47008411
## [29,] 0.079924578 -0.026678068 -0.13284266 -0.23682598 -0.33692062 -0.43148304
## [30,] 0.072037417 -0.024045408 -0.11973341 -0.21345539 -0.30367244 -0.38890320
## [31,] 0.064127132 -0.021405030 -0.10658572 -0.19001628 -0.27032678 -0.34619851
## [32,] 0.056660942 -0.018912886 -0.09417617 -0.16789308 -0.23885319 -0.30589133
## [33,] 0.049884941 -0.016651121 -0.08291377 -0.14781498 -0.21028907 -0.26931022
## [34,] 0.043886814 -0.014649003 -0.07294428 -0.13004182 -0.18500408 -0.23692857
## [35,] 0.038657629 -0.012903551 -0.06425285 -0.11454713 -0.16296054 -0.20869815
## [36,] 0.034138067 -0.011394964 -0.05674089 -0.10115513 -0.14390841 -0.18429872
## [37,] 0.030248053 -0.010096514 -0.05027530 -0.08962856 -0.12751012 -0.16329798
## [38,] 0.026903695 -0.008980199 -0.04471664 -0.07971883 -0.11341204 -0.14524303
## [39,] 0.024025916 -0.008019623 -0.03993348 -0.07119163 -0.10128082 -0.12970697
## [40,] 0.021544156 -0.007191236 -0.03580855 -0.06383788 -0.09081901 -0.11630888
## [41,] 0.019397384 -0.006474663 -0.03224040 -0.05747674 -0.08176932 -0.10471925
## [42,] 0.017533752 -0.005852600 -0.02914285 -0.05195458 -0.07391322 -0.09465820
## [43,] 0.015909672 -0.005310498 -0.02644347 -0.04714224 -0.06706694 -0.08589040
## [44,] 0.014488701 -0.004836191 -0.02408167 -0.04293173 -0.06107686 -0.07821910
## [45,] 0.013240434 -0.004419532 -0.02200693 -0.03923297 -0.05581481 -0.07148017
## [46,] 0.012139514 -0.004052055 -0.02017709 -0.03597082 -0.05117390 -0.06553672
## [47,] 0.011164766 -0.003726693 -0.01855696 -0.03308252 -0.04706487 -0.06027442
## [48,] 0.010298468 -0.003437531 -0.01711709 -0.03051558 -0.04341301 -0.05559760
## [49,] 0.009525749 -0.003179605 -0.01583275 -0.02822592 -0.04015562 -0.05142597
## [50,] 0.008834087 -0.002948735 -0.01468314 -0.02617644 -0.03723993 -0.04769194
##             [,43]       [,44]       [,45]       [,46]       [,47]       [,48]
##  [1,] -0.05736085 -0.06608790 -0.07372979 -0.08016103 -0.08527603 -0.08899081
##  [2,] -0.06185191 -0.07126224 -0.07950244 -0.08643722 -0.09195270 -0.09595832
##  [3,] -0.06686927 -0.07704296 -0.08595160 -0.09344892 -0.09941181 -0.10374236
##  [4,] -0.07249426 -0.08352374 -0.09318177 -0.10130976 -0.10777424 -0.11246907
##  [5,] -0.07882342 -0.09081584 -0.10131707 -0.11015468 -0.11718355 -0.12228827
##  [6,] -0.08597183 -0.09905184 -0.11050541 -0.12014449 -0.12781080 -0.13337846
##  [7,] -0.09407699 -0.10839014 -0.12092352 -0.13147134 -0.13986041 -0.14595297
##  [8,] -0.10330354 -0.11902044 -0.13278303 -0.14436532 -0.15357714 -0.16026723
##  [9,] -0.11384889 -0.13117020 -0.14633769 -0.15910231 -0.16925449 -0.17662751
## [10,] -0.12594970 -0.14511205 -0.16189166 -0.17601302 -0.18724425 -0.19540094
## [11,] -0.13988897 -0.16117208 -0.17980875 -0.19549297 -0.20796720 -0.21702661
## [12,] -0.15600335 -0.17973815 -0.20052166 -0.21801260 -0.23192379 -0.24202679
## [13,] -0.17468913 -0.20126685 -0.22453976 -0.24412574 -0.25970318 -0.27101630
## [14,] -0.19640448 -0.22628603 -0.25245196 -0.27447265 -0.29198650 -0.30470594
## [15,] -0.22166284 -0.25538727 -0.28491825 -0.30977087 -0.32953707 -0.34389228
## [16,] -0.25100894 -0.28919816 -0.32263877 -0.35078165 -0.37316471 -0.38942041
## [17,] -0.28496270 -0.32831775 -0.36628184 -0.39823158 -0.42364238 -0.44209697
## [18,] -0.32390931 -0.37318981 -0.41634255 -0.45265895 -0.48154270 -0.50251954
## [19,] -0.36790675 -0.42388115 -0.47289544 -0.51414479 -0.54695190 -0.57077808
## [20,] -0.41638568 -0.47973581 -0.53520868 -0.58189345 -0.61902354 -0.64598928
## [21,] -0.46774818 -0.53891274 -0.60122837 -0.65367185 -0.69538206 -0.72567411
## [22,] -0.51896052 -0.59791668 -0.66705506 -0.72524042 -0.77151735 -0.80512599
## [23,] -0.56538744 -0.65140713 -0.72673073 -0.79012143 -0.84053836 -0.87715367
## [24,] -0.60124633 -0.69272169 -0.77282259 -0.84023375 -0.89384830 -0.93278589
## [25,] -0.62093736 -0.71540858 -0.79813280 -0.86775170 -0.92312215 -0.96333496
## [26,] -0.62093736 -0.71540858 -0.79813280 -0.86775170 -0.92312215 -0.96333496
## [27,] -0.60124633 -0.69272169 -0.77282259 -0.84023375 -0.89384830 -0.93278589
## [28,] -0.56538744 -0.65140713 -0.72673073 -0.79012143 -0.84053836 -0.87715367
## [29,] -0.51896052 -0.59791668 -0.66705506 -0.72524042 -0.77151735 -0.80512599
## [30,] -0.46774818 -0.53891274 -0.60122837 -0.65367185 -0.69538206 -0.72567411
## [31,] -0.41638568 -0.47973581 -0.53520868 -0.58189345 -0.61902354 -0.64598928
## [32,] -0.36790675 -0.42388115 -0.47289544 -0.51414479 -0.54695190 -0.57077808
## [33,] -0.32390931 -0.37318981 -0.41634255 -0.45265895 -0.48154270 -0.50251954
## [34,] -0.28496270 -0.32831775 -0.36628184 -0.39823158 -0.42364238 -0.44209697
## [35,] -0.25100894 -0.28919816 -0.32263877 -0.35078165 -0.37316471 -0.38942041
## [36,] -0.22166284 -0.25538727 -0.28491825 -0.30977087 -0.32953707 -0.34389228
## [37,] -0.19640448 -0.22628603 -0.25245196 -0.27447265 -0.29198650 -0.30470594
## [38,] -0.17468913 -0.20126685 -0.22453976 -0.24412574 -0.25970318 -0.27101630
## [39,] -0.15600335 -0.17973815 -0.20052166 -0.21801260 -0.23192379 -0.24202679
## [40,] -0.13988897 -0.16117208 -0.17980875 -0.19549297 -0.20796720 -0.21702661
## [41,] -0.12594970 -0.14511205 -0.16189166 -0.17601302 -0.18724425 -0.19540094
## [42,] -0.11384889 -0.13117020 -0.14633769 -0.15910231 -0.16925449 -0.17662751
## [43,] -0.10330354 -0.11902044 -0.13278303 -0.14436532 -0.15357714 -0.16026723
## [44,] -0.09407699 -0.10839014 -0.12092352 -0.13147134 -0.13986041 -0.14595297
## [45,] -0.08597183 -0.09905184 -0.11050541 -0.12014449 -0.12781080 -0.13337846
## [46,] -0.07882342 -0.09081584 -0.10131707 -0.11015468 -0.11718355 -0.12228827
## [47,] -0.07249426 -0.08352374 -0.09318177 -0.10130976 -0.10777424 -0.11246907
## [48,] -0.06686927 -0.07704296 -0.08595160 -0.09344892 -0.09941181 -0.10374236
## [49,] -0.06185191 -0.07126224 -0.07950244 -0.08643722 -0.09195270 -0.09595832
## [50,] -0.05736085 -0.06608790 -0.07372979 -0.08016103 -0.08527603 -0.08899081
##             [,49]       [,50]
##  [1,] -0.09124435 -0.09199967
##  [2,] -0.09838830 -0.09920276
##  [3,] -0.10636947 -0.10724999
##  [4,] -0.11531717 -0.11627176
##  [5,] -0.12538502 -0.12642295
##  [6,] -0.13675606 -0.13788811
##  [7,] -0.14964899 -0.15088778
##  [8,] -0.16432573 -0.16568601
##  [9,] -0.18110031 -0.18259945
## [10,] -0.20034915 -0.20200763
## [11,] -0.22252245 -0.22436448
## [12,] -0.24815572 -0.25020994
## [13,] -0.27787935 -0.28017962
## [14,] -0.31242211 -0.31500833
## [15,] -0.35260078 -0.35551960
## [16,] -0.39928184 -0.40258707
## [17,] -0.45329235 -0.45704468
## [18,] -0.51524502 -0.51951019
## [19,] -0.58523209 -0.59007662
## [20,] -0.66234790 -0.66783078
## [21,] -0.74405061 -0.75020983
## [22,] -0.82551448 -0.83234804
## [23,] -0.89936615 -0.90681105
## [24,] -0.95640716 -0.96432424
## [25,] -0.98772983 -0.99590621
## [26,] -0.98772983 -0.99590621
## [27,] -0.95640716 -0.96432424
## [28,] -0.89936615 -0.90681105
## [29,] -0.82551448 -0.83234804
## [30,] -0.74405061 -0.75020983
## [31,] -0.66234790 -0.66783078
## [32,] -0.58523209 -0.59007662
## [33,] -0.51524502 -0.51951019
## [34,] -0.45329235 -0.45704468
## [35,] -0.39928184 -0.40258707
## [36,] -0.35260078 -0.35551960
## [37,] -0.31242211 -0.31500833
## [38,] -0.27787935 -0.28017962
## [39,] -0.24815572 -0.25020994
## [40,] -0.22252245 -0.22436448
## [41,] -0.20034915 -0.20200763
## [42,] -0.18110031 -0.18259945
## [43,] -0.16432573 -0.16568601
## [44,] -0.14964899 -0.15088778
## [45,] -0.13675606 -0.13788811
## [46,] -0.12538502 -0.12642295
## [47,] -0.11531717 -0.11627176
## [48,] -0.10636947 -0.10724999
## [49,] -0.09838830 -0.09920276
## [50,] -0.09124435 -0.09199967

contour(x, y, f)
contour(x,y,f,nlevels=45,add=T)

fa <- (f-t(f))/2
contour(x,y,fa,nlevels=15)

• image() to produce a color-coded plot whose colors depend on the z value (a.k.a. heatmap)

image(x,y,fa)

• persp() to produce a three-dimensional plot known as a heatmap, and is sometimes used to plot temperature in weather forecasts. Alternatively, persp() can be used to . The arguments theta and phi control the angles at which the plot is persp() viewed.

persp(x,y,fa)

persp(x,y,fa,theta=30)

persp(x,y,fa,theta=30,phi=20)

persp(x,y,fa,theta=30,phi=70)

persp(x,y,fa,theta=30,phi=40)

1.3 Indexing data

Examining a subset of a dataset A

A <- matrix(1:16,4,4)
A

##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16

A[2,3]

## [1] 10

A[c(1,3),c(2,4)]

##      [,1] [,2]
## [1,]    5   13
## [2,]    7   15

A[1:3,2:4]

##      [,1] [,2] [,3]
## [1,]    5    9   13
## [2,]    6   10   14
## [3,]    7   11   15

A[1,]

## [1]  1  5  9 13

A[1:2,]

##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14

A[,1:2]

##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8

A[-c(1,3),]

##      [,1] [,2] [,3] [,4]
## [1,]    2    6   10   14
## [2,]    4    8   12   16

dimensions

dim(A)

## [1] 4 4

1.4 Loading data

library(ISLR)
Auto

##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
##                                     name
## 1              chevrolet chevelle malibu
## 2                      buick skylark 320
## 3                     plymouth satellite
## 4                          amc rebel sst
## 5                            ford torino
## 6                       ford galaxie 500
## 7                       chevrolet impala
## 8                      plymouth fury iii
## 9                       pontiac catalina
## 10                    amc ambassador dpl
## 11                   dodge challenger se
## 12                    plymouth 'cuda 340
## 13                 chevrolet monte carlo
## 14               buick estate wagon (sw)
## 15                 toyota corona mark ii
## 16                       plymouth duster
## 17                            amc hornet
## 18                         ford maverick
## 19                          datsun pl510
## 20          volkswagen 1131 deluxe sedan
## 21                           peugeot 504
## 22                           audi 100 ls
## 23                              saab 99e
## 24                              bmw 2002
## 25                           amc gremlin
## 26                             ford f250
## 27                             chevy c20
## 28                            dodge d200
## 29                              hi 1200d
## 30                          datsun pl510
## 31                   chevrolet vega 2300
## 32                         toyota corona
## 34                           amc gremlin
## 35             plymouth satellite custom
## 36             chevrolet chevelle malibu
## 37                       ford torino 500
## 38                           amc matador
## 39                      chevrolet impala
## 40             pontiac catalina brougham
## 41                      ford galaxie 500
## 42                     plymouth fury iii
## 43                     dodge monaco (sw)
## 44              ford country squire (sw)
## 45                   pontiac safari (sw)
## 46            amc hornet sportabout (sw)
## 47                   chevrolet vega (sw)
## 48                      pontiac firebird
## 49                          ford mustang
## 50                    mercury capri 2000
## 51                             opel 1900
## 52                           peugeot 304
## 53                             fiat 124b
## 54                   toyota corolla 1200
## 55                           datsun 1200
## 56                  volkswagen model 111
## 57                      plymouth cricket
## 58                 toyota corona hardtop
## 59                    dodge colt hardtop
## 60                     volkswagen type 3
## 61                        chevrolet vega
## 62                   ford pinto runabout
## 63                      chevrolet impala
## 64                      pontiac catalina
## 65                     plymouth fury iii
## 66                      ford galaxie 500
## 67                    amc ambassador sst
## 68                       mercury marquis
## 69                  buick lesabre custom
## 70            oldsmobile delta 88 royale
## 71                chrysler newport royal
## 72                       mazda rx2 coupe
## 73                      amc matador (sw)
## 74      chevrolet chevelle concours (sw)
## 75                 ford gran torino (sw)
## 76        plymouth satellite custom (sw)
## 77                       volvo 145e (sw)
## 78                   volkswagen 411 (sw)
## 79                      peugeot 504 (sw)
## 80                       renault 12 (sw)
## 81                       ford pinto (sw)
## 82                       datsun 510 (sw)
## 83           toyouta corona mark ii (sw)
## 84                       dodge colt (sw)
## 85              toyota corolla 1600 (sw)
## 86                     buick century 350
## 87                           amc matador
## 88                      chevrolet malibu
## 89                      ford gran torino
## 90                  dodge coronet custom
## 91              mercury marquis brougham
## 92             chevrolet caprice classic
## 93                              ford ltd
## 94              plymouth fury gran sedan
## 95          chrysler new yorker brougham
## 96              buick electra 225 custom
## 97               amc ambassador brougham
## 98                      plymouth valiant
## 99                 chevrolet nova custom
## 100                           amc hornet
## 101                        ford maverick
## 102                      plymouth duster
## 103              volkswagen super beetle
## 104                     chevrolet impala
## 105                         ford country
## 106               plymouth custom suburb
## 107             oldsmobile vista cruiser
## 108                          amc gremlin
## 109                        toyota carina
## 110                       chevrolet vega
## 111                           datsun 610
## 112                            maxda rx3
## 113                           ford pinto
## 114                     mercury capri v6
## 115                 fiat 124 sport coupe
## 116              chevrolet monte carlo s
## 117                   pontiac grand prix
## 118                             fiat 128
## 119                           opel manta
## 120                           audi 100ls
## 121                          volvo 144ea
## 122                    dodge dart custom
## 123                            saab 99le
## 124                       toyota mark ii
## 125                     oldsmobile omega
## 126                      plymouth duster
## 128                           amc hornet
## 129                       chevrolet nova
## 130                          datsun b210
## 131                           ford pinto
## 132                  toyota corolla 1200
## 133                       chevrolet vega
## 134    chevrolet chevelle malibu classic
## 135                          amc matador
## 136           plymouth satellite sebring
## 137                     ford gran torino
## 138             buick century luxus (sw)
## 139            dodge coronet custom (sw)
## 140                ford gran torino (sw)
## 141                     amc matador (sw)
## 142                             audi fox
## 143                    volkswagen dasher
## 144                           opel manta
## 145                        toyota corona
## 146                           datsun 710
## 147                           dodge colt
## 148                             fiat 128
## 149                          fiat 124 tc
## 150                          honda civic
## 151                               subaru
## 152                            fiat x1.9
## 153              plymouth valiant custom
## 154                       chevrolet nova
## 155                      mercury monarch
## 156                        ford maverick
## 157                     pontiac catalina
## 158                    chevrolet bel air
## 159                  plymouth grand fury
## 160                             ford ltd
## 161                        buick century
## 162            chevroelt chevelle malibu
## 163                          amc matador
## 164                        plymouth fury
## 165                        buick skyhawk
## 166                  chevrolet monza 2+2
## 167                      ford mustang ii
## 168                       toyota corolla
## 169                           ford pinto
## 170                          amc gremlin
## 171                        pontiac astro
## 172                        toyota corona
## 173                    volkswagen dasher
## 174                           datsun 710
## 175                           ford pinto
## 176                    volkswagen rabbit
## 177                            amc pacer
## 178                           audi 100ls
## 179                          peugeot 504
## 180                          volvo 244dl
## 181                            saab 99le
## 182                     honda civic cvcc
## 183                             fiat 131
## 184                            opel 1900
## 185                             capri ii
## 186                           dodge colt
## 187                         renault 12tl
## 188    chevrolet chevelle malibu classic
## 189               dodge coronet brougham
## 190                          amc matador
## 191                     ford gran torino
## 192                     plymouth valiant
## 193                       chevrolet nova
## 194                        ford maverick
## 195                           amc hornet
## 196                   chevrolet chevette
## 197                      chevrolet woody
## 198                            vw rabbit
## 199                          honda civic
## 200                       dodge aspen se
## 201                    ford granada ghia
## 202                   pontiac ventura sj
## 203                        amc pacer d/l
## 204                    volkswagen rabbit
## 205                         datsun b-210
## 206                       toyota corolla
## 207                           ford pinto
## 208                            volvo 245
## 209           plymouth volare premier v8
## 210                          peugeot 504
## 211                       toyota mark ii
## 212                   mercedes-benz 280s
## 213                     cadillac seville
## 214                            chevy c10
## 215                            ford f108
## 216                           dodge d100
## 217                    honda accord cvcc
## 218              buick opel isuzu deluxe
## 219                        renault 5 gtl
## 220                    plymouth arrow gs
## 221                datsun f-10 hatchback
## 222            chevrolet caprice classic
## 223           oldsmobile cutlass supreme
## 224                dodge monaco brougham
## 225              mercury cougar brougham
## 226                   chevrolet concours
## 227                        buick skylark
## 228               plymouth volare custom
## 229                         ford granada
## 230                pontiac grand prix lj
## 231         chevrolet monte carlo landau
## 232                     chrysler cordoba
## 233                     ford thunderbird
## 234             volkswagen rabbit custom
## 235                pontiac sunbird coupe
## 236              toyota corolla liftback
## 237                  ford mustang ii 2+2
## 238                   chevrolet chevette
## 239                       dodge colt m/m
## 240                            subaru dl
## 241                    volkswagen dasher
## 242                           datsun 810
## 243                             bmw 320i
## 244                           mazda rx-4
## 245      volkswagen rabbit custom diesel
## 246                          ford fiesta
## 247                     mazda glc deluxe
## 248                       datsun b210 gx
## 249                     honda civic cvcc
## 250    oldsmobile cutlass salon brougham
## 251                       dodge diplomat
## 252                 mercury monarch ghia
## 253                   pontiac phoenix lj
## 254                     chevrolet malibu
## 255                 ford fairmont (auto)
## 256                  ford fairmont (man)
## 257                      plymouth volare
## 258                          amc concord
## 259                buick century special
## 260                       mercury zephyr
## 261                          dodge aspen
## 262                      amc concord d/l
## 263         chevrolet monte carlo landau
## 264      buick regal sport coupe (turbo)
## 265                          ford futura
## 266                      dodge magnum xe
## 267                   chevrolet chevette
## 268                        toyota corona
## 269                           datsun 510
## 270                           dodge omni
## 271            toyota celica gt liftback
## 272                     plymouth sapporo
## 273               oldsmobile starfire sx
## 274                        datsun 200-sx
## 275                            audi 5000
## 276                          volvo 264gl
## 277                           saab 99gle
## 278                        peugeot 604sl
## 279                  volkswagen scirocco
## 280                      honda accord lx
## 281                    pontiac lemans v6
## 282                     mercury zephyr 6
## 283                      ford fairmont 4
## 284                     amc concord dl 6
## 285                        dodge aspen 6
## 286            chevrolet caprice classic
## 287                      ford ltd landau
## 288                mercury grand marquis
## 289                      dodge st. regis
## 290              buick estate wagon (sw)
## 291             ford country squire (sw)
## 292        chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294                     vw rabbit custom
## 295                     maxda glc deluxe
## 296          dodge colt hatchback custom
## 297                        amc spirit dl
## 298                   mercedes benz 300d
## 299                    cadillac eldorado
## 300                          peugeot 504
## 301    oldsmobile cutlass salon brougham
## 302                     plymouth horizon
## 303                 plymouth horizon tc3
## 304                           datsun 210
## 305                   fiat strada custom
## 306                buick skylark limited
## 307                   chevrolet citation
## 308            oldsmobile omega brougham
## 309                      pontiac phoenix
## 310                            vw rabbit
## 311                toyota corolla tercel
## 312                   chevrolet chevette
## 313                           datsun 310
## 314                   chevrolet citation
## 315                        ford fairmont
## 316                          amc concord
## 317                          dodge aspen
## 318                            audi 4000
## 319               toyota corona liftback
## 320                            mazda 626
## 321                 datsun 510 hatchback
## 322                       toyota corolla
## 323                            mazda glc
## 324                           dodge colt
## 325                           datsun 210
## 326                 vw rabbit c (diesel)
## 327                   vw dasher (diesel)
## 328                  audi 5000s (diesel)
## 329                   mercedes-benz 240d
## 330                  honda civic 1500 gl
## 332                            subaru dl
## 333                     vokswagen rabbit
## 334                        datsun 280-zx
## 335                        mazda rx-7 gs
## 336                    triumph tr7 coupe
## 338                         honda accord
## 339                     plymouth reliant
## 340                        buick skylark
## 341               dodge aries wagon (sw)
## 342                   chevrolet citation
## 343                     plymouth reliant
## 344                       toyota starlet
## 345                       plymouth champ
## 346                     honda civic 1300
## 347                               subaru
## 348                       datsun 210 mpg
## 349                        toyota tercel
## 350                          mazda glc 4
## 351                   plymouth horizon 4
## 352                       ford escort 4w
## 353                       ford escort 2h
## 354                     volkswagen jetta
## 356                        honda prelude
## 357                       toyota corolla
## 358                         datsun 200sx
## 359                            mazda 626
## 360            peugeot 505s turbo diesel
## 361                         volvo diesel
## 362                      toyota cressida
## 363                    datsun 810 maxima
## 364                        buick century
## 365                oldsmobile cutlass ls
## 366                      ford granada gl
## 367               chrysler lebaron salon
## 368                   chevrolet cavalier
## 369             chevrolet cavalier wagon
## 370            chevrolet cavalier 2-door
## 371           pontiac j2000 se hatchback
## 372                       dodge aries se
## 373                      pontiac phoenix
## 374                 ford fairmont futura
## 375                  volkswagen rabbit l
## 376                   mazda glc custom l
## 377                     mazda glc custom
## 378               plymouth horizon miser
## 379                       mercury lynx l
## 380                     nissan stanza xe
## 381                         honda accord
## 382                       toyota corolla
## 383                          honda civic
## 384                   honda civic (auto)
## 385                        datsun 310 gx
## 386                buick century limited
## 387    oldsmobile cutlass ciera (diesel)
## 388           chrysler lebaron medallion
## 389                       ford granada l
## 390                     toyota celica gt
## 391                    dodge charger 2.2
## 392                     chevrolet camaro
## 393                      ford mustang gl
## 394                            vw pickup
## 395                        dodge rampage
## 396                          ford ranger
## 397                           chevy s-10

write.table(Auto, file = "Auto.txt")
read.table(file = "Auto.txt")

##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
##                                     name
## 1              chevrolet chevelle malibu
## 2                      buick skylark 320
## 3                     plymouth satellite
## 4                          amc rebel sst
## 5                            ford torino
## 6                       ford galaxie 500
## 7                       chevrolet impala
## 8                      plymouth fury iii
## 9                       pontiac catalina
## 10                    amc ambassador dpl
## 11                   dodge challenger se
## 12                    plymouth 'cuda 340
## 13                 chevrolet monte carlo
## 14               buick estate wagon (sw)
## 15                 toyota corona mark ii
## 16                       plymouth duster
## 17                            amc hornet
## 18                         ford maverick
## 19                          datsun pl510
## 20          volkswagen 1131 deluxe sedan
## 21                           peugeot 504
## 22                           audi 100 ls
## 23                              saab 99e
## 24                              bmw 2002
## 25                           amc gremlin
## 26                             ford f250
## 27                             chevy c20
## 28                            dodge d200
## 29                              hi 1200d
## 30                          datsun pl510
## 31                   chevrolet vega 2300
## 32                         toyota corona
## 34                           amc gremlin
## 35             plymouth satellite custom
## 36             chevrolet chevelle malibu
## 37                       ford torino 500
## 38                           amc matador
## 39                      chevrolet impala
## 40             pontiac catalina brougham
## 41                      ford galaxie 500
## 42                     plymouth fury iii
## 43                     dodge monaco (sw)
## 44              ford country squire (sw)
## 45                   pontiac safari (sw)
## 46            amc hornet sportabout (sw)
## 47                   chevrolet vega (sw)
## 48                      pontiac firebird
## 49                          ford mustang
## 50                    mercury capri 2000
## 51                             opel 1900
## 52                           peugeot 304
## 53                             fiat 124b
## 54                   toyota corolla 1200
## 55                           datsun 1200
## 56                  volkswagen model 111
## 57                      plymouth cricket
## 58                 toyota corona hardtop
## 59                    dodge colt hardtop
## 60                     volkswagen type 3
## 61                        chevrolet vega
## 62                   ford pinto runabout
## 63                      chevrolet impala
## 64                      pontiac catalina
## 65                     plymouth fury iii
## 66                      ford galaxie 500
## 67                    amc ambassador sst
## 68                       mercury marquis
## 69                  buick lesabre custom
## 70            oldsmobile delta 88 royale
## 71                chrysler newport royal
## 72                       mazda rx2 coupe
## 73                      amc matador (sw)
## 74      chevrolet chevelle concours (sw)
## 75                 ford gran torino (sw)
## 76        plymouth satellite custom (sw)
## 77                       volvo 145e (sw)
## 78                   volkswagen 411 (sw)
## 79                      peugeot 504 (sw)
## 80                       renault 12 (sw)
## 81                       ford pinto (sw)
## 82                       datsun 510 (sw)
## 83           toyouta corona mark ii (sw)
## 84                       dodge colt (sw)
## 85              toyota corolla 1600 (sw)
## 86                     buick century 350
## 87                           amc matador
## 88                      chevrolet malibu
## 89                      ford gran torino
## 90                  dodge coronet custom
## 91              mercury marquis brougham
## 92             chevrolet caprice classic
## 93                              ford ltd
## 94              plymouth fury gran sedan
## 95          chrysler new yorker brougham
## 96              buick electra 225 custom
## 97               amc ambassador brougham
## 98                      plymouth valiant
## 99                 chevrolet nova custom
## 100                           amc hornet
## 101                        ford maverick
## 102                      plymouth duster
## 103              volkswagen super beetle
## 104                     chevrolet impala
## 105                         ford country
## 106               plymouth custom suburb
## 107             oldsmobile vista cruiser
## 108                          amc gremlin
## 109                        toyota carina
## 110                       chevrolet vega
## 111                           datsun 610
## 112                            maxda rx3
## 113                           ford pinto
## 114                     mercury capri v6
## 115                 fiat 124 sport coupe
## 116              chevrolet monte carlo s
## 117                   pontiac grand prix
## 118                             fiat 128
## 119                           opel manta
## 120                           audi 100ls
## 121                          volvo 144ea
## 122                    dodge dart custom
## 123                            saab 99le
## 124                       toyota mark ii
## 125                     oldsmobile omega
## 126                      plymouth duster
## 128                           amc hornet
## 129                       chevrolet nova
## 130                          datsun b210
## 131                           ford pinto
## 132                  toyota corolla 1200
## 133                       chevrolet vega
## 134    chevrolet chevelle malibu classic
## 135                          amc matador
## 136           plymouth satellite sebring
## 137                     ford gran torino
## 138             buick century luxus (sw)
## 139            dodge coronet custom (sw)
## 140                ford gran torino (sw)
## 141                     amc matador (sw)
## 142                             audi fox
## 143                    volkswagen dasher
## 144                           opel manta
## 145                        toyota corona
## 146                           datsun 710
## 147                           dodge colt
## 148                             fiat 128
## 149                          fiat 124 tc
## 150                          honda civic
## 151                               subaru
## 152                            fiat x1.9
## 153              plymouth valiant custom
## 154                       chevrolet nova
## 155                      mercury monarch
## 156                        ford maverick
## 157                     pontiac catalina
## 158                    chevrolet bel air
## 159                  plymouth grand fury
## 160                             ford ltd
## 161                        buick century
## 162            chevroelt chevelle malibu
## 163                          amc matador
## 164                        plymouth fury
## 165                        buick skyhawk
## 166                  chevrolet monza 2+2
## 167                      ford mustang ii
## 168                       toyota corolla
## 169                           ford pinto
## 170                          amc gremlin
## 171                        pontiac astro
## 172                        toyota corona
## 173                    volkswagen dasher
## 174                           datsun 710
## 175                           ford pinto
## 176                    volkswagen rabbit
## 177                            amc pacer
## 178                           audi 100ls
## 179                          peugeot 504
## 180                          volvo 244dl
## 181                            saab 99le
## 182                     honda civic cvcc
## 183                             fiat 131
## 184                            opel 1900
## 185                             capri ii
## 186                           dodge colt
## 187                         renault 12tl
## 188    chevrolet chevelle malibu classic
## 189               dodge coronet brougham
## 190                          amc matador
## 191                     ford gran torino
## 192                     plymouth valiant
## 193                       chevrolet nova
## 194                        ford maverick
## 195                           amc hornet
## 196                   chevrolet chevette
## 197                      chevrolet woody
## 198                            vw rabbit
## 199                          honda civic
## 200                       dodge aspen se
## 201                    ford granada ghia
## 202                   pontiac ventura sj
## 203                        amc pacer d/l
## 204                    volkswagen rabbit
## 205                         datsun b-210
## 206                       toyota corolla
## 207                           ford pinto
## 208                            volvo 245
## 209           plymouth volare premier v8
## 210                          peugeot 504
## 211                       toyota mark ii
## 212                   mercedes-benz 280s
## 213                     cadillac seville
## 214                            chevy c10
## 215                            ford f108
## 216                           dodge d100
## 217                    honda accord cvcc
## 218              buick opel isuzu deluxe
## 219                        renault 5 gtl
## 220                    plymouth arrow gs
## 221                datsun f-10 hatchback
## 222            chevrolet caprice classic
## 223           oldsmobile cutlass supreme
## 224                dodge monaco brougham
## 225              mercury cougar brougham
## 226                   chevrolet concours
## 227                        buick skylark
## 228               plymouth volare custom
## 229                         ford granada
## 230                pontiac grand prix lj
## 231         chevrolet monte carlo landau
## 232                     chrysler cordoba
## 233                     ford thunderbird
## 234             volkswagen rabbit custom
## 235                pontiac sunbird coupe
## 236              toyota corolla liftback
## 237                  ford mustang ii 2+2
## 238                   chevrolet chevette
## 239                       dodge colt m/m
## 240                            subaru dl
## 241                    volkswagen dasher
## 242                           datsun 810
## 243                             bmw 320i
## 244                           mazda rx-4
## 245      volkswagen rabbit custom diesel
## 246                          ford fiesta
## 247                     mazda glc deluxe
## 248                       datsun b210 gx
## 249                     honda civic cvcc
## 250    oldsmobile cutlass salon brougham
## 251                       dodge diplomat
## 252                 mercury monarch ghia
## 253                   pontiac phoenix lj
## 254                     chevrolet malibu
## 255                 ford fairmont (auto)
## 256                  ford fairmont (man)
## 257                      plymouth volare
## 258                          amc concord
## 259                buick century special
## 260                       mercury zephyr
## 261                          dodge aspen
## 262                      amc concord d/l
## 263         chevrolet monte carlo landau
## 264      buick regal sport coupe (turbo)
## 265                          ford futura
## 266                      dodge magnum xe
## 267                   chevrolet chevette
## 268                        toyota corona
## 269                           datsun 510
## 270                           dodge omni
## 271            toyota celica gt liftback
## 272                     plymouth sapporo
## 273               oldsmobile starfire sx
## 274                        datsun 200-sx
## 275                            audi 5000
## 276                          volvo 264gl
## 277                           saab 99gle
## 278                        peugeot 604sl
## 279                  volkswagen scirocco
## 280                      honda accord lx
## 281                    pontiac lemans v6
## 282                     mercury zephyr 6
## 283                      ford fairmont 4
## 284                     amc concord dl 6
## 285                        dodge aspen 6
## 286            chevrolet caprice classic
## 287                      ford ltd landau
## 288                mercury grand marquis
## 289                      dodge st. regis
## 290              buick estate wagon (sw)
## 291             ford country squire (sw)
## 292        chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294                     vw rabbit custom
## 295                     maxda glc deluxe
## 296          dodge colt hatchback custom
## 297                        amc spirit dl
## 298                   mercedes benz 300d
## 299                    cadillac eldorado
## 300                          peugeot 504
## 301    oldsmobile cutlass salon brougham
## 302                     plymouth horizon
## 303                 plymouth horizon tc3
## 304                           datsun 210
## 305                   fiat strada custom
## 306                buick skylark limited
## 307                   chevrolet citation
## 308            oldsmobile omega brougham
## 309                      pontiac phoenix
## 310                            vw rabbit
## 311                toyota corolla tercel
## 312                   chevrolet chevette
## 313                           datsun 310
## 314                   chevrolet citation
## 315                        ford fairmont
## 316                          amc concord
## 317                          dodge aspen
## 318                            audi 4000
## 319               toyota corona liftback
## 320                            mazda 626
## 321                 datsun 510 hatchback
## 322                       toyota corolla
## 323                            mazda glc
## 324                           dodge colt
## 325                           datsun 210
## 326                 vw rabbit c (diesel)
## 327                   vw dasher (diesel)
## 328                  audi 5000s (diesel)
## 329                   mercedes-benz 240d
## 330                  honda civic 1500 gl
## 332                            subaru dl
## 333                     vokswagen rabbit
## 334                        datsun 280-zx
## 335                        mazda rx-7 gs
## 336                    triumph tr7 coupe
## 338                         honda accord
## 339                     plymouth reliant
## 340                        buick skylark
## 341               dodge aries wagon (sw)
## 342                   chevrolet citation
## 343                     plymouth reliant
## 344                       toyota starlet
## 345                       plymouth champ
## 346                     honda civic 1300
## 347                               subaru
## 348                       datsun 210 mpg
## 349                        toyota tercel
## 350                          mazda glc 4
## 351                   plymouth horizon 4
## 352                       ford escort 4w
## 353                       ford escort 2h
## 354                     volkswagen jetta
## 356                        honda prelude
## 357                       toyota corolla
## 358                         datsun 200sx
## 359                            mazda 626
## 360            peugeot 505s turbo diesel
## 361                         volvo diesel
## 362                      toyota cressida
## 363                    datsun 810 maxima
## 364                        buick century
## 365                oldsmobile cutlass ls
## 366                      ford granada gl
## 367               chrysler lebaron salon
## 368                   chevrolet cavalier
## 369             chevrolet cavalier wagon
## 370            chevrolet cavalier 2-door
## 371           pontiac j2000 se hatchback
## 372                       dodge aries se
## 373                      pontiac phoenix
## 374                 ford fairmont futura
## 375                  volkswagen rabbit l
## 376                   mazda glc custom l
## 377                     mazda glc custom
## 378               plymouth horizon miser
## 379                       mercury lynx l
## 380                     nissan stanza xe
## 381                         honda accord
## 382                       toyota corolla
## 383                          honda civic
## 384                   honda civic (auto)
## 385                        datsun 310 gx
## 386                buick century limited
## 387    oldsmobile cutlass ciera (diesel)
## 388           chrysler lebaron medallion
## 389                       ford granada l
## 390                     toyota celica gt
## 391                    dodge charger 2.2
## 392                     chevrolet camaro
## 393                      ford mustang gl
## 394                            vw pickup
## 395                        dodge rampage
## 396                          ford ranger
## 397                           chevy s-10

?read.csv

# fix(Auto)
View(Auto)
knitr::kable(Auto)

	mpg	cylinders	displacement	horsepower	weight	acceleration	year	origin	name
1	18.0	8	307.0	130	3504	12.0	70	1	chevrolet chevelle malibu
2	15.0	8	350.0	165	3693	11.5	70	1	buick skylark 320
3	18.0	8	318.0	150	3436	11.0	70	1	plymouth satellite
4	16.0	8	304.0	150	3433	12.0	70	1	amc rebel sst
5	17.0	8	302.0	140	3449	10.5	70	1	ford torino
6	15.0	8	429.0	198	4341	10.0	70	1	ford galaxie 500
7	14.0	8	454.0	220	4354	9.0	70	1	chevrolet impala
8	14.0	8	440.0	215	4312	8.5	70	1	plymouth fury iii
9	14.0	8	455.0	225	4425	10.0	70	1	pontiac catalina
10	15.0	8	390.0	190	3850	8.5	70	1	amc ambassador dpl
11	15.0	8	383.0	170	3563	10.0	70	1	dodge challenger se
12	14.0	8	340.0	160	3609	8.0	70	1	plymouth ’cuda 340
13	15.0	8	400.0	150	3761	9.5	70	1	chevrolet monte carlo
14	14.0	8	455.0	225	3086	10.0	70	1	buick estate wagon (sw)
15	24.0	4	113.0	95	2372	15.0	70	3	toyota corona mark ii
16	22.0	6	198.0	95	2833	15.5	70	1	plymouth duster
17	18.0	6	199.0	97	2774	15.5	70	1	amc hornet
18	21.0	6	200.0	85	2587	16.0	70	1	ford maverick
19	27.0	4	97.0	88	2130	14.5	70	3	datsun pl510
20	26.0	4	97.0	46	1835	20.5	70	2	volkswagen 1131 deluxe sedan
21	25.0	4	110.0	87	2672	17.5	70	2	peugeot 504
22	24.0	4	107.0	90	2430	14.5	70	2	audi 100 ls
23	25.0	4	104.0	95	2375	17.5	70	2	saab 99e
24	26.0	4	121.0	113	2234	12.5	70	2	bmw 2002
25	21.0	6	199.0	90	2648	15.0	70	1	amc gremlin
26	10.0	8	360.0	215	4615	14.0	70	1	ford f250
27	10.0	8	307.0	200	4376	15.0	70	1	chevy c20
28	11.0	8	318.0	210	4382	13.5	70	1	dodge d200
29	9.0	8	304.0	193	4732	18.5	70	1	hi 1200d
30	27.0	4	97.0	88	2130	14.5	71	3	datsun pl510
31	28.0	4	140.0	90	2264	15.5	71	1	chevrolet vega 2300
32	25.0	4	113.0	95	2228	14.0	71	3	toyota corona
34	19.0	6	232.0	100	2634	13.0	71	1	amc gremlin
35	16.0	6	225.0	105	3439	15.5	71	1	plymouth satellite custom
36	17.0	6	250.0	100	3329	15.5	71	1	chevrolet chevelle malibu
37	19.0	6	250.0	88	3302	15.5	71	1	ford torino 500
38	18.0	6	232.0	100	3288	15.5	71	1	amc matador
39	14.0	8	350.0	165	4209	12.0	71	1	chevrolet impala
40	14.0	8	400.0	175	4464	11.5	71	1	pontiac catalina brougham
41	14.0	8	351.0	153	4154	13.5	71	1	ford galaxie 500
42	14.0	8	318.0	150	4096	13.0	71	1	plymouth fury iii
43	12.0	8	383.0	180	4955	11.5	71	1	dodge monaco (sw)
44	13.0	8	400.0	170	4746	12.0	71	1	ford country squire (sw)
45	13.0	8	400.0	175	5140	12.0	71	1	pontiac safari (sw)
46	18.0	6	258.0	110	2962	13.5	71	1	amc hornet sportabout (sw)
47	22.0	4	140.0	72	2408	19.0	71	1	chevrolet vega (sw)
48	19.0	6	250.0	100	3282	15.0	71	1	pontiac firebird
49	18.0	6	250.0	88	3139	14.5	71	1	ford mustang
50	23.0	4	122.0	86	2220	14.0	71	1	mercury capri 2000
51	28.0	4	116.0	90	2123	14.0	71	2	opel 1900
52	30.0	4	79.0	70	2074	19.5	71	2	peugeot 304
53	30.0	4	88.0	76	2065	14.5	71	2	fiat 124b
54	31.0	4	71.0	65	1773	19.0	71	3	toyota corolla 1200
55	35.0	4	72.0	69	1613	18.0	71	3	datsun 1200
56	27.0	4	97.0	60	1834	19.0	71	2	volkswagen model 111
57	26.0	4	91.0	70	1955	20.5	71	1	plymouth cricket
58	24.0	4	113.0	95	2278	15.5	72	3	toyota corona hardtop
59	25.0	4	97.5	80	2126	17.0	72	1	dodge colt hardtop
60	23.0	4	97.0	54	2254	23.5	72	2	volkswagen type 3
61	20.0	4	140.0	90	2408	19.5	72	1	chevrolet vega
62	21.0	4	122.0	86	2226	16.5	72	1	ford pinto runabout
63	13.0	8	350.0	165	4274	12.0	72	1	chevrolet impala
64	14.0	8	400.0	175	4385	12.0	72	1	pontiac catalina
65	15.0	8	318.0	150	4135	13.5	72	1	plymouth fury iii
66	14.0	8	351.0	153	4129	13.0	72	1	ford galaxie 500
67	17.0	8	304.0	150	3672	11.5	72	1	amc ambassador sst
68	11.0	8	429.0	208	4633	11.0	72	1	mercury marquis
69	13.0	8	350.0	155	4502	13.5	72	1	buick lesabre custom
70	12.0	8	350.0	160	4456	13.5	72	1	oldsmobile delta 88 royale
71	13.0	8	400.0	190	4422	12.5	72	1	chrysler newport royal
72	19.0	3	70.0	97	2330	13.5	72	3	mazda rx2 coupe
73	15.0	8	304.0	150	3892	12.5	72	1	amc matador (sw)
74	13.0	8	307.0	130	4098	14.0	72	1	chevrolet chevelle concours (sw)
75	13.0	8	302.0	140	4294	16.0	72	1	ford gran torino (sw)
76	14.0	8	318.0	150	4077	14.0	72	1	plymouth satellite custom (sw)
77	18.0	4	121.0	112	2933	14.5	72	2	volvo 145e (sw)
78	22.0	4	121.0	76	2511	18.0	72	2	volkswagen 411 (sw)
79	21.0	4	120.0	87	2979	19.5	72	2	peugeot 504 (sw)
80	26.0	4	96.0	69	2189	18.0	72	2	renault 12 (sw)
81	22.0	4	122.0	86	2395	16.0	72	1	ford pinto (sw)
82	28.0	4	97.0	92	2288	17.0	72	3	datsun 510 (sw)
83	23.0	4	120.0	97	2506	14.5	72	3	toyouta corona mark ii (sw)
84	28.0	4	98.0	80	2164	15.0	72	1	dodge colt (sw)
85	27.0	4	97.0	88	2100	16.5	72	3	toyota corolla 1600 (sw)
86	13.0	8	350.0	175	4100	13.0	73	1	buick century 350
87	14.0	8	304.0	150	3672	11.5	73	1	amc matador
88	13.0	8	350.0	145	3988	13.0	73	1	chevrolet malibu
89	14.0	8	302.0	137	4042	14.5	73	1	ford gran torino
90	15.0	8	318.0	150	3777	12.5	73	1	dodge coronet custom
91	12.0	8	429.0	198	4952	11.5	73	1	mercury marquis brougham
92	13.0	8	400.0	150	4464	12.0	73	1	chevrolet caprice classic
93	13.0	8	351.0	158	4363	13.0	73	1	ford ltd
94	14.0	8	318.0	150	4237	14.5	73	1	plymouth fury gran sedan
95	13.0	8	440.0	215	4735	11.0	73	1	chrysler new yorker brougham
96	12.0	8	455.0	225	4951	11.0	73	1	buick electra 225 custom
97	13.0	8	360.0	175	3821	11.0	73	1	amc ambassador brougham
98	18.0	6	225.0	105	3121	16.5	73	1	plymouth valiant
99	16.0	6	250.0	100	3278	18.0	73	1	chevrolet nova custom
100	18.0	6	232.0	100	2945	16.0	73	1	amc hornet
101	18.0	6	250.0	88	3021	16.5	73	1	ford maverick
102	23.0	6	198.0	95	2904	16.0	73	1	plymouth duster
103	26.0	4	97.0	46	1950	21.0	73	2	volkswagen super beetle
104	11.0	8	400.0	150	4997	14.0	73	1	chevrolet impala
105	12.0	8	400.0	167	4906	12.5	73	1	ford country
106	13.0	8	360.0	170	4654	13.0	73	1	plymouth custom suburb
107	12.0	8	350.0	180	4499	12.5	73	1	oldsmobile vista cruiser
108	18.0	6	232.0	100	2789	15.0	73	1	amc gremlin
109	20.0	4	97.0	88	2279	19.0	73	3	toyota carina
110	21.0	4	140.0	72	2401	19.5	73	1	chevrolet vega
111	22.0	4	108.0	94	2379	16.5	73	3	datsun 610
112	18.0	3	70.0	90	2124	13.5	73	3	maxda rx3
113	19.0	4	122.0	85	2310	18.5	73	1	ford pinto
114	21.0	6	155.0	107	2472	14.0	73	1	mercury capri v6
115	26.0	4	98.0	90	2265	15.5	73	2	fiat 124 sport coupe
116	15.0	8	350.0	145	4082	13.0	73	1	chevrolet monte carlo s
117	16.0	8	400.0	230	4278	9.5	73	1	pontiac grand prix
118	29.0	4	68.0	49	1867	19.5	73	2	fiat 128
119	24.0	4	116.0	75	2158	15.5	73	2	opel manta
120	20.0	4	114.0	91	2582	14.0	73	2	audi 100ls
121	19.0	4	121.0	112	2868	15.5	73	2	volvo 144ea
122	15.0	8	318.0	150	3399	11.0	73	1	dodge dart custom
123	24.0	4	121.0	110	2660	14.0	73	2	saab 99le
124	20.0	6	156.0	122	2807	13.5	73	3	toyota mark ii
125	11.0	8	350.0	180	3664	11.0	73	1	oldsmobile omega
126	20.0	6	198.0	95	3102	16.5	74	1	plymouth duster
128	19.0	6	232.0	100	2901	16.0	74	1	amc hornet
129	15.0	6	250.0	100	3336	17.0	74	1	chevrolet nova
130	31.0	4	79.0	67	1950	19.0	74	3	datsun b210
131	26.0	4	122.0	80	2451	16.5	74	1	ford pinto
132	32.0	4	71.0	65	1836	21.0	74	3	toyota corolla 1200
133	25.0	4	140.0	75	2542	17.0	74	1	chevrolet vega
134	16.0	6	250.0	100	3781	17.0	74	1	chevrolet chevelle malibu classic
135	16.0	6	258.0	110	3632	18.0	74	1	amc matador
136	18.0	6	225.0	105	3613	16.5	74	1	plymouth satellite sebring
137	16.0	8	302.0	140	4141	14.0	74	1	ford gran torino
138	13.0	8	350.0	150	4699	14.5	74	1	buick century luxus (sw)
139	14.0	8	318.0	150	4457	13.5	74	1	dodge coronet custom (sw)
140	14.0	8	302.0	140	4638	16.0	74	1	ford gran torino (sw)
141	14.0	8	304.0	150	4257	15.5	74	1	amc matador (sw)
142	29.0	4	98.0	83	2219	16.5	74	2	audi fox
143	26.0	4	79.0	67	1963	15.5	74	2	volkswagen dasher
144	26.0	4	97.0	78	2300	14.5	74	2	opel manta
145	31.0	4	76.0	52	1649	16.5	74	3	toyota corona
146	32.0	4	83.0	61	2003	19.0	74	3	datsun 710
147	28.0	4	90.0	75	2125	14.5	74	1	dodge colt
148	24.0	4	90.0	75	2108	15.5	74	2	fiat 128
149	26.0	4	116.0	75	2246	14.0	74	2	fiat 124 tc
150	24.0	4	120.0	97	2489	15.0	74	3	honda civic
151	26.0	4	108.0	93	2391	15.5	74	3	subaru
152	31.0	4	79.0	67	2000	16.0	74	2	fiat x1.9
153	19.0	6	225.0	95	3264	16.0	75	1	plymouth valiant custom
154	18.0	6	250.0	105	3459	16.0	75	1	chevrolet nova
155	15.0	6	250.0	72	3432	21.0	75	1	mercury monarch
156	15.0	6	250.0	72	3158	19.5	75	1	ford maverick
157	16.0	8	400.0	170	4668	11.5	75	1	pontiac catalina
158	15.0	8	350.0	145	4440	14.0	75	1	chevrolet bel air
159	16.0	8	318.0	150	4498	14.5	75	1	plymouth grand fury
160	14.0	8	351.0	148	4657	13.5	75	1	ford ltd
161	17.0	6	231.0	110	3907	21.0	75	1	buick century
162	16.0	6	250.0	105	3897	18.5	75	1	chevroelt chevelle malibu
163	15.0	6	258.0	110	3730	19.0	75	1	amc matador
164	18.0	6	225.0	95	3785	19.0	75	1	plymouth fury
165	21.0	6	231.0	110	3039	15.0	75	1	buick skyhawk
166	20.0	8	262.0	110	3221	13.5	75	1	chevrolet monza 2+2
167	13.0	8	302.0	129	3169	12.0	75	1	ford mustang ii
168	29.0	4	97.0	75	2171	16.0	75	3	toyota corolla
169	23.0	4	140.0	83	2639	17.0	75	1	ford pinto
170	20.0	6	232.0	100	2914	16.0	75	1	amc gremlin
171	23.0	4	140.0	78	2592	18.5	75	1	pontiac astro
172	24.0	4	134.0	96	2702	13.5	75	3	toyota corona
173	25.0	4	90.0	71	2223	16.5	75	2	volkswagen dasher
174	24.0	4	119.0	97	2545	17.0	75	3	datsun 710
175	18.0	6	171.0	97	2984	14.5	75	1	ford pinto
176	29.0	4	90.0	70	1937	14.0	75	2	volkswagen rabbit
177	19.0	6	232.0	90	3211	17.0	75	1	amc pacer
178	23.0	4	115.0	95	2694	15.0	75	2	audi 100ls
179	23.0	4	120.0	88	2957	17.0	75	2	peugeot 504
180	22.0	4	121.0	98	2945	14.5	75	2	volvo 244dl
181	25.0	4	121.0	115	2671	13.5	75	2	saab 99le
182	33.0	4	91.0	53	1795	17.5	75	3	honda civic cvcc
183	28.0	4	107.0	86	2464	15.5	76	2	fiat 131
184	25.0	4	116.0	81	2220	16.9	76	2	opel 1900
185	25.0	4	140.0	92	2572	14.9	76	1	capri ii
186	26.0	4	98.0	79	2255	17.7	76	1	dodge colt
187	27.0	4	101.0	83	2202	15.3	76	2	renault 12tl
188	17.5	8	305.0	140	4215	13.0	76	1	chevrolet chevelle malibu classic
189	16.0	8	318.0	150	4190	13.0	76	1	dodge coronet brougham
190	15.5	8	304.0	120	3962	13.9	76	1	amc matador
191	14.5	8	351.0	152	4215	12.8	76	1	ford gran torino
192	22.0	6	225.0	100	3233	15.4	76	1	plymouth valiant
193	22.0	6	250.0	105	3353	14.5	76	1	chevrolet nova
194	24.0	6	200.0	81	3012	17.6	76	1	ford maverick
195	22.5	6	232.0	90	3085	17.6	76	1	amc hornet
196	29.0	4	85.0	52	2035	22.2	76	1	chevrolet chevette
197	24.5	4	98.0	60	2164	22.1	76	1	chevrolet woody
198	29.0	4	90.0	70	1937	14.2	76	2	vw rabbit
199	33.0	4	91.0	53	1795	17.4	76	3	honda civic
200	20.0	6	225.0	100	3651	17.7	76	1	dodge aspen se
201	18.0	6	250.0	78	3574	21.0	76	1	ford granada ghia
202	18.5	6	250.0	110	3645	16.2	76	1	pontiac ventura sj
203	17.5	6	258.0	95	3193	17.8	76	1	amc pacer d/l
204	29.5	4	97.0	71	1825	12.2	76	2	volkswagen rabbit
205	32.0	4	85.0	70	1990	17.0	76	3	datsun b-210
206	28.0	4	97.0	75	2155	16.4	76	3	toyota corolla
207	26.5	4	140.0	72	2565	13.6	76	1	ford pinto
208	20.0	4	130.0	102	3150	15.7	76	2	volvo 245
209	13.0	8	318.0	150	3940	13.2	76	1	plymouth volare premier v8
210	19.0	4	120.0	88	3270	21.9	76	2	peugeot 504
211	19.0	6	156.0	108	2930	15.5	76	3	toyota mark ii
212	16.5	6	168.0	120	3820	16.7	76	2	mercedes-benz 280s
213	16.5	8	350.0	180	4380	12.1	76	1	cadillac seville
214	13.0	8	350.0	145	4055	12.0	76	1	chevy c10
215	13.0	8	302.0	130	3870	15.0	76	1	ford f108
216	13.0	8	318.0	150	3755	14.0	76	1	dodge d100
217	31.5	4	98.0	68	2045	18.5	77	3	honda accord cvcc
218	30.0	4	111.0	80	2155	14.8	77	1	buick opel isuzu deluxe
219	36.0	4	79.0	58	1825	18.6	77	2	renault 5 gtl
220	25.5	4	122.0	96	2300	15.5	77	1	plymouth arrow gs
221	33.5	4	85.0	70	1945	16.8	77	3	datsun f-10 hatchback
222	17.5	8	305.0	145	3880	12.5	77	1	chevrolet caprice classic
223	17.0	8	260.0	110	4060	19.0	77	1	oldsmobile cutlass supreme
224	15.5	8	318.0	145	4140	13.7	77	1	dodge monaco brougham
225	15.0	8	302.0	130	4295	14.9	77	1	mercury cougar brougham
226	17.5	6	250.0	110	3520	16.4	77	1	chevrolet concours
227	20.5	6	231.0	105	3425	16.9	77	1	buick skylark
228	19.0	6	225.0	100	3630	17.7	77	1	plymouth volare custom
229	18.5	6	250.0	98	3525	19.0	77	1	ford granada
230	16.0	8	400.0	180	4220	11.1	77	1	pontiac grand prix lj
231	15.5	8	350.0	170	4165	11.4	77	1	chevrolet monte carlo landau
232	15.5	8	400.0	190	4325	12.2	77	1	chrysler cordoba
233	16.0	8	351.0	149	4335	14.5	77	1	ford thunderbird
234	29.0	4	97.0	78	1940	14.5	77	2	volkswagen rabbit custom
235	24.5	4	151.0	88	2740	16.0	77	1	pontiac sunbird coupe
236	26.0	4	97.0	75	2265	18.2	77	3	toyota corolla liftback
237	25.5	4	140.0	89	2755	15.8	77	1	ford mustang ii 2+2
238	30.5	4	98.0	63	2051	17.0	77	1	chevrolet chevette
239	33.5	4	98.0	83	2075	15.9	77	1	dodge colt m/m
240	30.0	4	97.0	67	1985	16.4	77	3	subaru dl
241	30.5	4	97.0	78	2190	14.1	77	2	volkswagen dasher
242	22.0	6	146.0	97	2815	14.5	77	3	datsun 810
243	21.5	4	121.0	110	2600	12.8	77	2	bmw 320i
244	21.5	3	80.0	110	2720	13.5	77	3	mazda rx-4
245	43.1	4	90.0	48	1985	21.5	78	2	volkswagen rabbit custom diesel
246	36.1	4	98.0	66	1800	14.4	78	1	ford fiesta
247	32.8	4	78.0	52	1985	19.4	78	3	mazda glc deluxe
248	39.4	4	85.0	70	2070	18.6	78	3	datsun b210 gx
249	36.1	4	91.0	60	1800	16.4	78	3	honda civic cvcc
250	19.9	8	260.0	110	3365	15.5	78	1	oldsmobile cutlass salon brougham
251	19.4	8	318.0	140	3735	13.2	78	1	dodge diplomat
252	20.2	8	302.0	139	3570	12.8	78	1	mercury monarch ghia
253	19.2	6	231.0	105	3535	19.2	78	1	pontiac phoenix lj
254	20.5	6	200.0	95	3155	18.2	78	1	chevrolet malibu
255	20.2	6	200.0	85	2965	15.8	78	1	ford fairmont (auto)
256	25.1	4	140.0	88	2720	15.4	78	1	ford fairmont (man)
257	20.5	6	225.0	100	3430	17.2	78	1	plymouth volare
258	19.4	6	232.0	90	3210	17.2	78	1	amc concord
259	20.6	6	231.0	105	3380	15.8	78	1	buick century special
260	20.8	6	200.0	85	3070	16.7	78	1	mercury zephyr
261	18.6	6	225.0	110	3620	18.7	78	1	dodge aspen
262	18.1	6	258.0	120	3410	15.1	78	1	amc concord d/l
263	19.2	8	305.0	145	3425	13.2	78	1	chevrolet monte carlo landau
264	17.7	6	231.0	165	3445	13.4	78	1	buick regal sport coupe (turbo)
265	18.1	8	302.0	139	3205	11.2	78	1	ford futura
266	17.5	8	318.0	140	4080	13.7	78	1	dodge magnum xe
267	30.0	4	98.0	68	2155	16.5	78	1	chevrolet chevette
268	27.5	4	134.0	95	2560	14.2	78	3	toyota corona
269	27.2	4	119.0	97	2300	14.7	78	3	datsun 510
270	30.9	4	105.0	75	2230	14.5	78	1	dodge omni
271	21.1	4	134.0	95	2515	14.8	78	3	toyota celica gt liftback
272	23.2	4	156.0	105	2745	16.7	78	1	plymouth sapporo
273	23.8	4	151.0	85	2855	17.6	78	1	oldsmobile starfire sx
274	23.9	4	119.0	97	2405	14.9	78	3	datsun 200-sx
275	20.3	5	131.0	103	2830	15.9	78	2	audi 5000
276	17.0	6	163.0	125	3140	13.6	78	2	volvo 264gl
277	21.6	4	121.0	115	2795	15.7	78	2	saab 99gle
278	16.2	6	163.0	133	3410	15.8	78	2	peugeot 604sl
279	31.5	4	89.0	71	1990	14.9	78	2	volkswagen scirocco
280	29.5	4	98.0	68	2135	16.6	78	3	honda accord lx
281	21.5	6	231.0	115	3245	15.4	79	1	pontiac lemans v6
282	19.8	6	200.0	85	2990	18.2	79	1	mercury zephyr 6
283	22.3	4	140.0	88	2890	17.3	79	1	ford fairmont 4
284	20.2	6	232.0	90	3265	18.2	79	1	amc concord dl 6
285	20.6	6	225.0	110	3360	16.6	79	1	dodge aspen 6
286	17.0	8	305.0	130	3840	15.4	79	1	chevrolet caprice classic
287	17.6	8	302.0	129	3725	13.4	79	1	ford ltd landau
288	16.5	8	351.0	138	3955	13.2	79	1	mercury grand marquis
289	18.2	8	318.0	135	3830	15.2	79	1	dodge st. regis
290	16.9	8	350.0	155	4360	14.9	79	1	buick estate wagon (sw)
291	15.5	8	351.0	142	4054	14.3	79	1	ford country squire (sw)
292	19.2	8	267.0	125	3605	15.0	79	1	chevrolet malibu classic (sw)
293	18.5	8	360.0	150	3940	13.0	79	1	chrysler lebaron town @ country (sw)
294	31.9	4	89.0	71	1925	14.0	79	2	vw rabbit custom
295	34.1	4	86.0	65	1975	15.2	79	3	maxda glc deluxe
296	35.7	4	98.0	80	1915	14.4	79	1	dodge colt hatchback custom
297	27.4	4	121.0	80	2670	15.0	79	1	amc spirit dl
298	25.4	5	183.0	77	3530	20.1	79	2	mercedes benz 300d
299	23.0	8	350.0	125	3900	17.4	79	1	cadillac eldorado
300	27.2	4	141.0	71	3190	24.8	79	2	peugeot 504
301	23.9	8	260.0	90	3420	22.2	79	1	oldsmobile cutlass salon brougham
302	34.2	4	105.0	70	2200	13.2	79	1	plymouth horizon
303	34.5	4	105.0	70	2150	14.9	79	1	plymouth horizon tc3
304	31.8	4	85.0	65	2020	19.2	79	3	datsun 210
305	37.3	4	91.0	69	2130	14.7	79	2	fiat strada custom
306	28.4	4	151.0	90	2670	16.0	79	1	buick skylark limited
307	28.8	6	173.0	115	2595	11.3	79	1	chevrolet citation
308	26.8	6	173.0	115	2700	12.9	79	1	oldsmobile omega brougham
309	33.5	4	151.0	90	2556	13.2	79	1	pontiac phoenix
310	41.5	4	98.0	76	2144	14.7	80	2	vw rabbit
311	38.1	4	89.0	60	1968	18.8	80	3	toyota corolla tercel
312	32.1	4	98.0	70	2120	15.5	80	1	chevrolet chevette
313	37.2	4	86.0	65	2019	16.4	80	3	datsun 310
314	28.0	4	151.0	90	2678	16.5	80	1	chevrolet citation
315	26.4	4	140.0	88	2870	18.1	80	1	ford fairmont
316	24.3	4	151.0	90	3003	20.1	80	1	amc concord
317	19.1	6	225.0	90	3381	18.7	80	1	dodge aspen
318	34.3	4	97.0	78	2188	15.8	80	2	audi 4000
319	29.8	4	134.0	90	2711	15.5	80	3	toyota corona liftback
320	31.3	4	120.0	75	2542	17.5	80	3	mazda 626
321	37.0	4	119.0	92	2434	15.0	80	3	datsun 510 hatchback
322	32.2	4	108.0	75	2265	15.2	80	3	toyota corolla
323	46.6	4	86.0	65	2110	17.9	80	3	mazda glc
324	27.9	4	156.0	105	2800	14.4	80	1	dodge colt
325	40.8	4	85.0	65	2110	19.2	80	3	datsun 210
326	44.3	4	90.0	48	2085	21.7	80	2	vw rabbit c (diesel)
327	43.4	4	90.0	48	2335	23.7	80	2	vw dasher (diesel)
328	36.4	5	121.0	67	2950	19.9	80	2	audi 5000s (diesel)
329	30.0	4	146.0	67	3250	21.8	80	2	mercedes-benz 240d
330	44.6	4	91.0	67	1850	13.8	80	3	honda civic 1500 gl
332	33.8	4	97.0	67	2145	18.0	80	3	subaru dl
333	29.8	4	89.0	62	1845	15.3	80	2	vokswagen rabbit
334	32.7	6	168.0	132	2910	11.4	80	3	datsun 280-zx
335	23.7	3	70.0	100	2420	12.5	80	3	mazda rx-7 gs
336	35.0	4	122.0	88	2500	15.1	80	2	triumph tr7 coupe
338	32.4	4	107.0	72	2290	17.0	80	3	honda accord
339	27.2	4	135.0	84	2490	15.7	81	1	plymouth reliant
340	26.6	4	151.0	84	2635	16.4	81	1	buick skylark
341	25.8	4	156.0	92	2620	14.4	81	1	dodge aries wagon (sw)
342	23.5	6	173.0	110	2725	12.6	81	1	chevrolet citation
343	30.0	4	135.0	84	2385	12.9	81	1	plymouth reliant
344	39.1	4	79.0	58	1755	16.9	81	3	toyota starlet
345	39.0	4	86.0	64	1875	16.4	81	1	plymouth champ
346	35.1	4	81.0	60	1760	16.1	81	3	honda civic 1300
347	32.3	4	97.0	67	2065	17.8	81	3	subaru
348	37.0	4	85.0	65	1975	19.4	81	3	datsun 210 mpg
349	37.7	4	89.0	62	2050	17.3	81	3	toyota tercel
350	34.1	4	91.0	68	1985	16.0	81	3	mazda glc 4
351	34.7	4	105.0	63	2215	14.9	81	1	plymouth horizon 4
352	34.4	4	98.0	65	2045	16.2	81	1	ford escort 4w
353	29.9	4	98.0	65	2380	20.7	81	1	ford escort 2h
354	33.0	4	105.0	74	2190	14.2	81	2	volkswagen jetta
356	33.7	4	107.0	75	2210	14.4	81	3	honda prelude
357	32.4	4	108.0	75	2350	16.8	81	3	toyota corolla
358	32.9	4	119.0	100	2615	14.8	81	3	datsun 200sx
359	31.6	4	120.0	74	2635	18.3	81	3	mazda 626
360	28.1	4	141.0	80	3230	20.4	81	2	peugeot 505s turbo diesel
361	30.7	6	145.0	76	3160	19.6	81	2	volvo diesel
362	25.4	6	168.0	116	2900	12.6	81	3	toyota cressida
363	24.2	6	146.0	120	2930	13.8	81	3	datsun 810 maxima
364	22.4	6	231.0	110	3415	15.8	81	1	buick century
365	26.6	8	350.0	105	3725	19.0	81	1	oldsmobile cutlass ls
366	20.2	6	200.0	88	3060	17.1	81	1	ford granada gl
367	17.6	6	225.0	85	3465	16.6	81	1	chrysler lebaron salon
368	28.0	4	112.0	88	2605	19.6	82	1	chevrolet cavalier
369	27.0	4	112.0	88	2640	18.6	82	1	chevrolet cavalier wagon
370	34.0	4	112.0	88	2395	18.0	82	1	chevrolet cavalier 2-door
371	31.0	4	112.0	85	2575	16.2	82	1	pontiac j2000 se hatchback
372	29.0	4	135.0	84	2525	16.0	82	1	dodge aries se
373	27.0	4	151.0	90	2735	18.0	82	1	pontiac phoenix
374	24.0	4	140.0	92	2865	16.4	82	1	ford fairmont futura
375	36.0	4	105.0	74	1980	15.3	82	2	volkswagen rabbit l
376	37.0	4	91.0	68	2025	18.2	82	3	mazda glc custom l
377	31.0	4	91.0	68	1970	17.6	82	3	mazda glc custom
378	38.0	4	105.0	63	2125	14.7	82	1	plymouth horizon miser
379	36.0	4	98.0	70	2125	17.3	82	1	mercury lynx l
380	36.0	4	120.0	88	2160	14.5	82	3	nissan stanza xe
381	36.0	4	107.0	75	2205	14.5	82	3	honda accord
382	34.0	4	108.0	70	2245	16.9	82	3	toyota corolla
383	38.0	4	91.0	67	1965	15.0	82	3	honda civic
384	32.0	4	91.0	67	1965	15.7	82	3	honda civic (auto)
385	38.0	4	91.0	67	1995	16.2	82	3	datsun 310 gx
386	25.0	6	181.0	110	2945	16.4	82	1	buick century limited
387	38.0	6	262.0	85	3015	17.0	82	1	oldsmobile cutlass ciera (diesel)
388	26.0	4	156.0	92	2585	14.5	82	1	chrysler lebaron medallion
389	22.0	6	232.0	112	2835	14.7	82	1	ford granada l
390	32.0	4	144.0	96	2665	13.9	82	3	toyota celica gt
391	36.0	4	135.0	84	2370	13.0	82	1	dodge charger 2.2
392	27.0	4	151.0	90	2950	17.3	82	1	chevrolet camaro
393	27.0	4	140.0	86	2790	15.6	82	1	ford mustang gl
394	44.0	4	97.0	52	2130	24.6	82	2	vw pickup
395	32.0	4	135.0	84	2295	11.6	82	1	dodge rampage
396	28.0	4	120.0	79	2625	18.6	82	1	ford ranger
397	31.0	4	119.0	82	2720	19.4	82	1	chevy s-10

class(Auto)

## [1] "data.frame"

dim(Auto)

## [1] 392   9

names(Auto)

## [1] "mpg"          "cylinders"    "displacement" "horsepower"   "weight"      
## [6] "acceleration" "year"         "origin"       "name"

str(Auto)

## 'data.frame':    392 obs. of  9 variables:
##  $ mpg         : num  18 15 18 16 17 15 14 14 14 15 ...
##  $ cylinders   : num  8 8 8 8 8 8 8 8 8 8 ...
##  $ displacement: num  307 350 318 304 302 429 454 440 455 390 ...
##  $ horsepower  : num  130 165 150 150 140 198 220 215 225 190 ...
##  $ weight      : num  3504 3693 3436 3433 3449 ...
##  $ acceleration: num  12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
##  $ year        : num  70 70 70 70 70 70 70 70 70 70 ...
##  $ origin      : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ name        : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...

na.omit(Auto)

##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
##                                     name
## 1              chevrolet chevelle malibu
## 2                      buick skylark 320
## 3                     plymouth satellite
## 4                          amc rebel sst
## 5                            ford torino
## 6                       ford galaxie 500
## 7                       chevrolet impala
## 8                      plymouth fury iii
## 9                       pontiac catalina
## 10                    amc ambassador dpl
## 11                   dodge challenger se
## 12                    plymouth 'cuda 340
## 13                 chevrolet monte carlo
## 14               buick estate wagon (sw)
## 15                 toyota corona mark ii
## 16                       plymouth duster
## 17                            amc hornet
## 18                         ford maverick
## 19                          datsun pl510
## 20          volkswagen 1131 deluxe sedan
## 21                           peugeot 504
## 22                           audi 100 ls
## 23                              saab 99e
## 24                              bmw 2002
## 25                           amc gremlin
## 26                             ford f250
## 27                             chevy c20
## 28                            dodge d200
## 29                              hi 1200d
## 30                          datsun pl510
## 31                   chevrolet vega 2300
## 32                         toyota corona
## 34                           amc gremlin
## 35             plymouth satellite custom
## 36             chevrolet chevelle malibu
## 37                       ford torino 500
## 38                           amc matador
## 39                      chevrolet impala
## 40             pontiac catalina brougham
## 41                      ford galaxie 500
## 42                     plymouth fury iii
## 43                     dodge monaco (sw)
## 44              ford country squire (sw)
## 45                   pontiac safari (sw)
## 46            amc hornet sportabout (sw)
## 47                   chevrolet vega (sw)
## 48                      pontiac firebird
## 49                          ford mustang
## 50                    mercury capri 2000
## 51                             opel 1900
## 52                           peugeot 304
## 53                             fiat 124b
## 54                   toyota corolla 1200
## 55                           datsun 1200
## 56                  volkswagen model 111
## 57                      plymouth cricket
## 58                 toyota corona hardtop
## 59                    dodge colt hardtop
## 60                     volkswagen type 3
## 61                        chevrolet vega
## 62                   ford pinto runabout
## 63                      chevrolet impala
## 64                      pontiac catalina
## 65                     plymouth fury iii
## 66                      ford galaxie 500
## 67                    amc ambassador sst
## 68                       mercury marquis
## 69                  buick lesabre custom
## 70            oldsmobile delta 88 royale
## 71                chrysler newport royal
## 72                       mazda rx2 coupe
## 73                      amc matador (sw)
## 74      chevrolet chevelle concours (sw)
## 75                 ford gran torino (sw)
## 76        plymouth satellite custom (sw)
## 77                       volvo 145e (sw)
## 78                   volkswagen 411 (sw)
## 79                      peugeot 504 (sw)
## 80                       renault 12 (sw)
## 81                       ford pinto (sw)
## 82                       datsun 510 (sw)
## 83           toyouta corona mark ii (sw)
## 84                       dodge colt (sw)
## 85              toyota corolla 1600 (sw)
## 86                     buick century 350
## 87                           amc matador
## 88                      chevrolet malibu
## 89                      ford gran torino
## 90                  dodge coronet custom
## 91              mercury marquis brougham
## 92             chevrolet caprice classic
## 93                              ford ltd
## 94              plymouth fury gran sedan
## 95          chrysler new yorker brougham
## 96              buick electra 225 custom
## 97               amc ambassador brougham
## 98                      plymouth valiant
## 99                 chevrolet nova custom
## 100                           amc hornet
## 101                        ford maverick
## 102                      plymouth duster
## 103              volkswagen super beetle
## 104                     chevrolet impala
## 105                         ford country
## 106               plymouth custom suburb
## 107             oldsmobile vista cruiser
## 108                          amc gremlin
## 109                        toyota carina
## 110                       chevrolet vega
## 111                           datsun 610
## 112                            maxda rx3
## 113                           ford pinto
## 114                     mercury capri v6
## 115                 fiat 124 sport coupe
## 116              chevrolet monte carlo s
## 117                   pontiac grand prix
## 118                             fiat 128
## 119                           opel manta
## 120                           audi 100ls
## 121                          volvo 144ea
## 122                    dodge dart custom
## 123                            saab 99le
## 124                       toyota mark ii
## 125                     oldsmobile omega
## 126                      plymouth duster
## 128                           amc hornet
## 129                       chevrolet nova
## 130                          datsun b210
## 131                           ford pinto
## 132                  toyota corolla 1200
## 133                       chevrolet vega
## 134    chevrolet chevelle malibu classic
## 135                          amc matador
## 136           plymouth satellite sebring
## 137                     ford gran torino
## 138             buick century luxus (sw)
## 139            dodge coronet custom (sw)
## 140                ford gran torino (sw)
## 141                     amc matador (sw)
## 142                             audi fox
## 143                    volkswagen dasher
## 144                           opel manta
## 145                        toyota corona
## 146                           datsun 710
## 147                           dodge colt
## 148                             fiat 128
## 149                          fiat 124 tc
## 150                          honda civic
## 151                               subaru
## 152                            fiat x1.9
## 153              plymouth valiant custom
## 154                       chevrolet nova
## 155                      mercury monarch
## 156                        ford maverick
## 157                     pontiac catalina
## 158                    chevrolet bel air
## 159                  plymouth grand fury
## 160                             ford ltd
## 161                        buick century
## 162            chevroelt chevelle malibu
## 163                          amc matador
## 164                        plymouth fury
## 165                        buick skyhawk
## 166                  chevrolet monza 2+2
## 167                      ford mustang ii
## 168                       toyota corolla
## 169                           ford pinto
## 170                          amc gremlin
## 171                        pontiac astro
## 172                        toyota corona
## 173                    volkswagen dasher
## 174                           datsun 710
## 175                           ford pinto
## 176                    volkswagen rabbit
## 177                            amc pacer
## 178                           audi 100ls
## 179                          peugeot 504
## 180                          volvo 244dl
## 181                            saab 99le
## 182                     honda civic cvcc
## 183                             fiat 131
## 184                            opel 1900
## 185                             capri ii
## 186                           dodge colt
## 187                         renault 12tl
## 188    chevrolet chevelle malibu classic
## 189               dodge coronet brougham
## 190                          amc matador
## 191                     ford gran torino
## 192                     plymouth valiant
## 193                       chevrolet nova
## 194                        ford maverick
## 195                           amc hornet
## 196                   chevrolet chevette
## 197                      chevrolet woody
## 198                            vw rabbit
## 199                          honda civic
## 200                       dodge aspen se
## 201                    ford granada ghia
## 202                   pontiac ventura sj
## 203                        amc pacer d/l
## 204                    volkswagen rabbit
## 205                         datsun b-210
## 206                       toyota corolla
## 207                           ford pinto
## 208                            volvo 245
## 209           plymouth volare premier v8
## 210                          peugeot 504
## 211                       toyota mark ii
## 212                   mercedes-benz 280s
## 213                     cadillac seville
## 214                            chevy c10
## 215                            ford f108
## 216                           dodge d100
## 217                    honda accord cvcc
## 218              buick opel isuzu deluxe
## 219                        renault 5 gtl
## 220                    plymouth arrow gs
## 221                datsun f-10 hatchback
## 222            chevrolet caprice classic
## 223           oldsmobile cutlass supreme
## 224                dodge monaco brougham
## 225              mercury cougar brougham
## 226                   chevrolet concours
## 227                        buick skylark
## 228               plymouth volare custom
## 229                         ford granada
## 230                pontiac grand prix lj
## 231         chevrolet monte carlo landau
## 232                     chrysler cordoba
## 233                     ford thunderbird
## 234             volkswagen rabbit custom
## 235                pontiac sunbird coupe
## 236              toyota corolla liftback
## 237                  ford mustang ii 2+2
## 238                   chevrolet chevette
## 239                       dodge colt m/m
## 240                            subaru dl
## 241                    volkswagen dasher
## 242                           datsun 810
## 243                             bmw 320i
## 244                           mazda rx-4
## 245      volkswagen rabbit custom diesel
## 246                          ford fiesta
## 247                     mazda glc deluxe
## 248                       datsun b210 gx
## 249                     honda civic cvcc
## 250    oldsmobile cutlass salon brougham
## 251                       dodge diplomat
## 252                 mercury monarch ghia
## 253                   pontiac phoenix lj
## 254                     chevrolet malibu
## 255                 ford fairmont (auto)
## 256                  ford fairmont (man)
## 257                      plymouth volare
## 258                          amc concord
## 259                buick century special
## 260                       mercury zephyr
## 261                          dodge aspen
## 262                      amc concord d/l
## 263         chevrolet monte carlo landau
## 264      buick regal sport coupe (turbo)
## 265                          ford futura
## 266                      dodge magnum xe
## 267                   chevrolet chevette
## 268                        toyota corona
## 269                           datsun 510
## 270                           dodge omni
## 271            toyota celica gt liftback
## 272                     plymouth sapporo
## 273               oldsmobile starfire sx
## 274                        datsun 200-sx
## 275                            audi 5000
## 276                          volvo 264gl
## 277                           saab 99gle
## 278                        peugeot 604sl
## 279                  volkswagen scirocco
## 280                      honda accord lx
## 281                    pontiac lemans v6
## 282                     mercury zephyr 6
## 283                      ford fairmont 4
## 284                     amc concord dl 6
## 285                        dodge aspen 6
## 286            chevrolet caprice classic
## 287                      ford ltd landau
## 288                mercury grand marquis
## 289                      dodge st. regis
## 290              buick estate wagon (sw)
## 291             ford country squire (sw)
## 292        chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294                     vw rabbit custom
## 295                     maxda glc deluxe
## 296          dodge colt hatchback custom
## 297                        amc spirit dl
## 298                   mercedes benz 300d
## 299                    cadillac eldorado
## 300                          peugeot 504
## 301    oldsmobile cutlass salon brougham
## 302                     plymouth horizon
## 303                 plymouth horizon tc3
## 304                           datsun 210
## 305                   fiat strada custom
## 306                buick skylark limited
## 307                   chevrolet citation
## 308            oldsmobile omega brougham
## 309                      pontiac phoenix
## 310                            vw rabbit
## 311                toyota corolla tercel
## 312                   chevrolet chevette
## 313                           datsun 310
## 314                   chevrolet citation
## 315                        ford fairmont
## 316                          amc concord
## 317                          dodge aspen
## 318                            audi 4000
## 319               toyota corona liftback
## 320                            mazda 626
## 321                 datsun 510 hatchback
## 322                       toyota corolla
## 323                            mazda glc
## 324                           dodge colt
## 325                           datsun 210
## 326                 vw rabbit c (diesel)
## 327                   vw dasher (diesel)
## 328                  audi 5000s (diesel)
## 329                   mercedes-benz 240d
## 330                  honda civic 1500 gl
## 332                            subaru dl
## 333                     vokswagen rabbit
## 334                        datsun 280-zx
## 335                        mazda rx-7 gs
## 336                    triumph tr7 coupe
## 338                         honda accord
## 339                     plymouth reliant
## 340                        buick skylark
## 341               dodge aries wagon (sw)
## 342                   chevrolet citation
## 343                     plymouth reliant
## 344                       toyota starlet
## 345                       plymouth champ
## 346                     honda civic 1300
## 347                               subaru
## 348                       datsun 210 mpg
## 349                        toyota tercel
## 350                          mazda glc 4
## 351                   plymouth horizon 4
## 352                       ford escort 4w
## 353                       ford escort 2h
## 354                     volkswagen jetta
## 356                        honda prelude
## 357                       toyota corolla
## 358                         datsun 200sx
## 359                            mazda 626
## 360            peugeot 505s turbo diesel
## 361                         volvo diesel
## 362                      toyota cressida
## 363                    datsun 810 maxima
## 364                        buick century
## 365                oldsmobile cutlass ls
## 366                      ford granada gl
## 367               chrysler lebaron salon
## 368                   chevrolet cavalier
## 369             chevrolet cavalier wagon
## 370            chevrolet cavalier 2-door
## 371           pontiac j2000 se hatchback
## 372                       dodge aries se
## 373                      pontiac phoenix
## 374                 ford fairmont futura
## 375                  volkswagen rabbit l
## 376                   mazda glc custom l
## 377                     mazda glc custom
## 378               plymouth horizon miser
## 379                       mercury lynx l
## 380                     nissan stanza xe
## 381                         honda accord
## 382                       toyota corolla
## 383                          honda civic
## 384                   honda civic (auto)
## 385                        datsun 310 gx
## 386                buick century limited
## 387    oldsmobile cutlass ciera (diesel)
## 388           chrysler lebaron medallion
## 389                       ford granada l
## 390                     toyota celica gt
## 391                    dodge charger 2.2
## 392                     chevrolet camaro
## 393                      ford mustang gl
## 394                            vw pickup
## 395                        dodge rampage
## 396                          ford ranger
## 397                           chevy s-10

dim(na.omit(Auto))

## [1] 392   9

1.5 Additional summaries

Scatterplot of quantitative variables

plot(cylinders , mpg)

## Error in plot(cylinders, mpg): object 'cylinders' not found

To refer to a variable, we must type the data set and the variable name joined with a $ symbol.

DO NOT USE attach()

plot(Auto$cylinders, Auto$mpg)

plot(Auto$cylinders)

# but this is actually a factor...

Auto$cylinders <- as.factor(Auto$cylinders)
plot(Auto$cylinders, Auto$mpg)

plot(Auto$cylinders)

# customizing the aspect
plot(Auto$cylinders, Auto$mpg, col="red", varwidth=T, xlab="cylinders", ylab = "MPG")

plot(Auto$cylinders, Auto$mpg, col="red", horizontal=T, xlab="cylinders", ylab = "MPG")

Histogram

hist(Auto$mpg)

hist(Auto$mpg, col = 2)

hist(Auto$mpg, breaks=15)

Scatterplot matrix

pairs(Auto)

# for just a subset
pairs(~mpg + displacement + horsepower + weight, Auto)

identify(): a useful interactive method for identifying the value for a particular variable for points on a plot.

plot(Auto$horsepower, Auto$mpg)
identify(Auto$horsepower,Auto$mpg,Auto$name)

## integer(0)

# click, click, click, and then ESC

One of your best friends: summary(), to produce a numerical summary of each variable in a particular data set

summary(Auto)

##       mpg        cylinders  displacement     horsepower        weight    
##  Min.   : 9.00   3:  4     Min.   : 68.0   Min.   : 46.0   Min.   :1613  
##  1st Qu.:17.00   4:199     1st Qu.:105.0   1st Qu.: 75.0   1st Qu.:2225  
##  Median :22.75   5:  3     Median :151.0   Median : 93.5   Median :2804  
##  Mean   :23.45   6: 83     Mean   :194.4   Mean   :104.5   Mean   :2978  
##  3rd Qu.:29.00   8:103     3rd Qu.:275.8   3rd Qu.:126.0   3rd Qu.:3615  
##  Max.   :46.60             Max.   :455.0   Max.   :230.0   Max.   :5140  
##                                                                          
##   acceleration        year           origin                      name    
##  Min.   : 8.00   Min.   :70.00   Min.   :1.000   amc matador       :  5  
##  1st Qu.:13.78   1st Qu.:73.00   1st Qu.:1.000   ford pinto        :  5  
##  Median :15.50   Median :76.00   Median :1.000   toyota corolla    :  5  
##  Mean   :15.54   Mean   :75.98   Mean   :1.577   amc gremlin       :  4  
##  3rd Qu.:17.02   3rd Qu.:79.00   3rd Qu.:2.000   amc hornet        :  4  
##  Max.   :24.80   Max.   :82.00   Max.   :3.000   chevrolet chevette:  4  
##                                                  (Other)           :365

summary(Auto$mpg)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    9.00   17.00   22.75   23.45   29.00   46.60

summary(Auto$cylinders)

##   3   4   5   6   8 
##   4 199   3  83 103

Done for today

q()
quit()

but first, you can savehistory("history_filename.R") - still, I would recommend to always use a script anyway!

2 Chapter 2 Exercises

2.4 Exercises Conceptual 1. For each of parts (a) through (d), indicate whether we would generally expect the performance of a flexible statistical learning method to be better or worse than an inflexible method. Justify your answer. (a) The sample size n is extremely large, and the number of predic- tors p is small. (b) The number of predictors p is extremely large, and the number of observations n is small. (c) The relationship between the predictors and response is highly non-linear. (d) The variance of the error terms, i.e. σ2 = Var(ε), is extremely high. 2. Explain whether each scenario is a classification or regression prob- lem, and indicate whether we are most interested in inference or pre- diction. Finally, provide n and p. (a) We collect a set of data on the top 500 firms in the US. For each firm we record profit, number of employees, industry and the CEO salary. We are interested in understanding which factors affect CEO salary. (b) We are considering launching a new product and wish to know whether it will be a success or a failure. We collect data on 20 similar products that were previously launched. For each prod- uct we have recorded whether it was a success or failure, price charged for the product, marketing budget, competition price, and ten other variables. (c) We are interested in predicting the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. Hence we collect weekly data for all of 2012. For each week we record the % change in the USD/Euro, the % change in the US market, the % change in the British market, and the % change in the German market. 3. We now revisit the bias-variance decomposition. (a) Provide a sketch of typical (squared) bias, variance, training er- ror, test error, and Bayes (or irreducible) error curves, on a sin- gle plot, as we go from less flexible statistical learning methods towards more flexible approaches. The x-axis should represent 4. You ing. will now think of some real-life applications for statistical learn- the amount of flexibility in the method, and the y-axis should represent the values for each curve. There should be five curves. Make sure to label each one. (b) Explain why each of the five curves has the shape displayed in part (a). (a) Describe three real-life applications in which classification might be useful. Describe the response, as well as the predictors. Is the goal of each application inference or prediction? Explain your answer. (b) Describe three real-life applications in which regression might be useful. Describe the response, as well as the predictors. Is the goal of each application inference or prediction? Explain your answer. (c) Describe three real-life applications in which cluster analysis might be useful. 5. What are the advantages and disadvantages of a very flexible (versus a less flexible) approach for regression or classification? Under what circumstances might a more flexible approach be preferred to a less flexible approach? When might a less flexible approach be preferred? 6. Describe the differences between a parametric and a non-parametric statistical learning approach. What are the advantages of a para- metric approach to regression or classification (as opposed to a non- parametric approach)? What are its disadvantages? 7. The table below provides a training data set containing six observa- tions, three predictors, and one qualitative response variable. Obs. X1 X2 X3 Y 1 030Red 2 200Red 3 013Red 4 012Green 5 −1 0 1 Green 6 111Red Suppose we wish to use this data set to make a prediction for Y when X1 = X2 = X3 = 0 using K-nearest neighbors. (a) Compute the Euclidean distance between each observation and thetestpoint,X1 =X2 =X3 =0.

2.4 Exercises 53

54 2. Statistical Learning (b) What is our prediction with K = 1? Why? (c) What is our prediction with K = 3? Why? (d) If the Bayes decision boundary in this problem is highly non- linear, then would we expect the best value for K to be large or small? Why? Applied 8. This exercise relates to the College data set, which can be found in the file College.csv. It contains a number of variables for 777 different universities and colleges in the US. The variables are • Private : Public/private indicator • Apps : Number of applications received • Accept : Number of applicants accepted • Enroll : Number of new students enrolled • Top10perc : New students from top 10 % of high school class • Top25perc : New students from top 25 % of high school class • F.Undergrad : Number of full-time undergraduates • P.Undergrad : Number of part-time undergraduates • Outstate : Out-of-state tuition • Room.Board : Room and board costs • Books : Estimated book costs • Personal : Estimated personal spending • PhD : Percent of faculty with Ph.D.’s • Terminal : Percent of faculty with terminal degree • S.F.Ratio : Student/faculty ratio • perc.alumni : Percent of alumni who donate • Expend : Instructional expenditure per student • Grad.Rate : Graduation rate Before reading the data into R, it can be viewed in Excel or a text editor. (a) Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data. (b) Look at the data using the fix() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands: 2.4 Exercises 55 (c) > rownames(college)=college[,1] > fix(college) You should see that there is now a row.names column with the name of each university recorded. This means that R has given each row a name corresponding to the appropriate university. R will not try to perform calculations on the row names. However, we still need to eliminate the first column in the data where the names are stored. Try > college=college[,-1] > fix(college) Now you should see that the first data column is Private. Note that another column labeled row.names now appears before the Private column. However, this is not a data column but rather the name that R is giving to each row. i. Use the summary() function to produce a numerical summary of the variables in the data set. ii. Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10]. iii. Use the plot() function to produce side-by-side boxplots of Outstate versus Private. iv. Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10% of their high school classes exceeds 50 %. > Elite=rep(“No”,nrow(college)) > Elite[college$Top10perc >50]=“Yes” > Elite=as.factor(Elite) > college=data.frame(college ,Elite) Use the summary() function to see how many elite univer- sities there are. Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite. v. Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative vari- ables. You may find the command par(mfrow=c(2,2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways. vi. Continue exploring the data, and provide a brief summary of what you discover.

56 2. Statistical Learning 9. This exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data. (a) Which of the predictors are quantitative, and which are quali- tative? (b) What is the range of each quantitative predictor? You can an- swer this using the range() function. (c) What is the mean and standard deviation of each quantitative predictor? (d) Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains? (e) Using the full data set, investigate the predictors graphically, using scatterplots or other tools of your choice. Create some plots highlighting the relationships among the predictors. Comment on your findings. (f) Suppose that we wish to predict gas mileage (mpg) on the basis of the other variables. Do your plots suggest that any of the other variables might be useful in predicting mpg? Justify your answer. 10. This exercise involves the Boston housing data set. (a) To begin, load in the Boston data set. The Boston data set is part of the MASS library in R. > library(MASS) Now the data set is contained in the object Boston. > Boston Read about the data set: > ?Boston How many rows are in this data set? How many columns? What do the rows and columns represent? (b) Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings. (c) Are any of the predictors associated with per capita crime rate? If so, explain the relationship. (d) Do any of the suburbs of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor. (e) How many of the suburbs in this data set bound the Charles river? range()

6. What is the median pupil-teacher ratio among the towns in this data set?
7. Which suburb of Boston has lowest median value of owner- occupied homes? What are the values of the other predictors for that suburb, and how do those values compare to the overall ranges for those predictors? Comment on your findings.
8. In this data set, how many of the suburbs average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the suburbs that average more than eight rooms per dwelling.